thermophysical and mechanical … · thermophysical and mechanical ... the goal of this project is...

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Università di Pisa

DIPARTIMENTO DI INGEGNERIA CIVILE E INDUSTRIALE

Corso di Laurea Magistrale in Ingegneria Meccanica

THERMOPHYSICAL AND MECHANICAL

CHARACTERIZATION OF ADVANCED MATERIALS

FOR THE LHC COLLIMATION SYSTEM

Relatori: Laureanda:

Ch.mo Prof. Ing. Renzo Valentini Laura Bianchi

Ing. Michael Guinchard

II Appello anno 2017

Anno accademico 2015/2016

Acknowledgments

I would like to express my gratitude towards my supervisor at CERN, Eng. Michael Guinchard,

who provided me trust and guidance during the months of internship in his laboratory, and to

my thesis advisor Prof. Eng. Renzo Valentini of the University of Pisa for the valuable advices

and support.

My colleagues added value to the work done, both for the scientific and cultural consultations,

the professional recommendations and the friendly environment. Among them, I want to thank

all the member of the MML of the EN department (Eugénie, Philippe, Morgane, Lucile, Luigi,

Roland and Lukasz), particularly Óscar Sacristan de Frutos, for the constant availability and

teachings. I wish to thank also Alessandro, Federico, Jorge and Inigo, for the daily exchange of

information and collaboration.

At the end of this part of my life, I can say that school years would not have been the same

without my friends Alice C., Alice L., Claudio, Leonardo, Margherita and Mattia, incomparable

mates who shared with me intense days of study and cheerful moments.

Thanks to all the relatives and to the closer people, a source of encouragement and joy.

My life path could not have been possible without the day-by-day love, support and patience

dispensed by my parents, Andrea and Maria Letizia, and my boyfriend, Andrea, who helped

me facing any obstacle and gave me the most sincere and benevolent advices.

Ringraziamenti

Vorrei ringraziare il mio Professore Ing. Renzo Valentini dell’Università di Pisa, relatore di

questa tesi, per avermi fornito supporto e consigli utili durante la redazione del lavoro e il mio

supervisore al CERN, Ing. Michael Guinchard, per la sua guida e la fiducia riposta in me durante

i mesi di stage presso il suo laboratorio di misure meccaniche.

Sono riconoscente a tutti i colleghi che, grazie agli scambi di opinioni scientifiche e culturali,

ai consigli professionali e all’ambiente amichevole che hanno saputo creare attorno a me sin

dal mio arrivo, hanno contribuito alla realizzazione della tesi. Ringrazio dunque tutti i membri

del laboratorio di misure meccaniche del Dipartimento di Ingegneria (Eugénie, Philippe,

Morgane, Lucile, Luigi, Roland e Lukasz) ed in particolar modo Óscar Sacristan de Frutos, mio

mentore, per i dialoghi e gli insegnamenti quotidiani. Tra gli altri, ci tengo a ringraziare

Alessandro, Federico, Jorge e Inigo per gli scambi di informazioni e la collaborazione

quotidiana.

Ringrazio gli amici (di infanzia e di università), che hanno reso gli anni di studio più leggeri e

mi sono rimasti vicini, nonostante la lontananza: Alice C., Alice L., Claudio, Leonardo,

Margherita e Mattia.

Ringrazio i parenti e le persone che sono state al mio fianco e hanno creduto in me.

Infine, il mio ringraziamento più grande va ai miei genitori, Maria Letizia e Andrea, e al mio

ragazzo, Andrea. Il loro amore e i loro consigli sono stati indispensabili: mi hanno dato la forza

di inseguire i miei sogni, affrontare gli ostacoli ed intraprendere le mie scelte.

Abstract

The aim of the thesis is to describe the methods employed for the thermo-physical and

mechanical characterization and to show the results of the campaign conducted over two

ceramic matrix composites, CFC FS140® and MG-6403-Fc, which are candidates as jaws

materials in the LHC collimation system. The work was conducted at the European

Organization for Nuclear Research (CERN, Geneva), in the framework of the R&D activities

done by the EN department. The goal of this project is to develop and characterize materials

able to withstand highly energetic particles interactions to protect the accelerator’s components

and to clean the beam. In the first part of the thesis, the instruments employed for the thermal

and mechanical analysis are studied, from the mathematical models to the standard test

methods. These instruments are: horizontal push-rod dilatometer, differential scanning

calorimeter, laser flash apparatus and universal testing machine. The results of the analysis

show lower thermal and electrical conductivities of the CFC chosen, with respect with the one

currently in use. The MoGR grade is in line with the previously developed ones, suggesting

further improvement in the manufacturing process. The status of the collimators materials’

development process after these characterization, sees the MoGR as baseline material for the

primary and secondary collimators and the CFC to produce spares. Carrying out the campaign

had been of paramount importance in understanding the physical principles and the technology

behind the techniques, and to acquire experience in the thermo-physical and mechanical test

engineering.

Riassunto

Lo scopo della tesi è quello di descrivere le tecniche impiegate per la caratterizzazione

termofisica e meccanica di materiali innovativi nell’ambito della fisica nucleare, oltre a quello

di presentare i risultati ottenuti dalla campagna su due compositi. Il lavoro, svolto presso

l’Organizzazione Europea per la Ricerca Nucleare (CERN) di Ginevra, rientra nel progetto di

ricerca e sviluppo finalizzato alla realizzazione di compositi avanzati per le ganasce dei

collimatori dell’LHC. I test sono stati eseguiti nel Laboratorio di misure meccaniche della

sezione EN-MME-EDM per mezzo di una macchina universale di trazione, un calorimetro

differenziale a scansione, un dilatometro orizzontale e un apparato laser flash. I materiali

investigati sono due compositi a matrice grafitica rinforzati l’uno con fibre di carbonio (CFC

FS140®) e l’altro con carburi di molibdeno (MoGR, MG-6403-Fc). I risultati ottenuti mostrano

come il CFC testato abbia conducibilità termica ed elettrica inferiori rispetto a quello

attualmente impiegato nei collimatori, verosimilmente a causa dell’insufficiente temperatura

finale di grafitizzazione. MG-6403-Fc mostra proprietà intermedie fra quelle dei due più

promettenti gradi di MoGR finora sviluppati. La caratterizzazione svolta su questi due materiali

ha permesso di ottenere importanti informazioni per il progetto di collimazione e di

programmare le prossime tappe del lavoro di ricerca, oltre ad acquisire una più profonda

conoscenza delle tecniche e un approccio critico alla scienza della misura.

Index

Introduction ................................................................................................................................. I

Background .............................................................................................................................. I

CERN: European Organization for Nuclear Research ........................................................ I

CERN’s accelerator complex ............................................................................................ II

The LHC ........................................................................................................................... III

The Collimation system .................................................................................................... IV

Aim and structure of the thesis ............................................................................................. VI

1 State of the art: materials .................................................................................................... 1

1.1 Figures of Merit ........................................................................................................... 1

1.2 Graphite ....................................................................................................................... 3

1.3 Ceramic matrix composites.......................................................................................... 4

1.4 Conventional reference system .................................................................................... 5

1.5 Carbon fiber – Carbon composites .............................................................................. 5

1.5.1 CFC fields of use .................................................................................................. 5

1.5.2 CFC AC150® ........................................................................................................ 6

1.6 Molybdenum carbide – Graphite composites .............................................................. 7

1.6.1 R&D ..................................................................................................................... 7

1.6.2 MoGR ................................................................................................................... 8

1.7 Current collimator materials ...................................................................................... 12

2 State of the art: methods ................................................................................................... 14

2.1 Thermo-physical properties and their measurement .................................................. 14

2.1.1 Specific heat ....................................................................................................... 14

2.1.2 Methods for measuring the specific heat ............................................................ 15

2.1.3 Coefficient of thermal expansion ....................................................................... 17

2.1.4 Methods for measuring the coefficient of thermal expansion ............................ 19

2.1.5 Energy balance equation, thermal conductivity and thermal diffusivity ............ 22

2.1.6 Methods for measuring thermal conductivity ..................................................... 24

2.2 Mechanical properties and their measurement .......................................................... 31

2.2.1 Mechanical properties......................................................................................... 31

2.2.2 Methods for measuring the mechanical properties ............................................. 33

3 Experimental work: materials and methods ..................................................................... 40

3.1 Materials .................................................................................................................... 40

3.1.1 CFC FS140® ....................................................................................................... 40

3.1.2 MG-6403-Fc ....................................................................................................... 42

3.2 Instruments for the thermo-physical analysis ............................................................ 43

3.2.1 Push-rod dilatometer: DIL 402 E ....................................................................... 43

3.2.2 Laser flash apparatus: LFA 427.......................................................................... 47

3.2.3 Differential scanning calorimeter: DSC Pegasus 404C ...................................... 50

3.3 Instruments for the mechanical characterization ....................................................... 52

3.3.1 Universal testing machine: Zwick/Roell Z400 ................................................... 52

3.3.2 Impact excitation technique ................................................................................ 56

4 Results .............................................................................................................................. 58

4.1 CFC FS140® .............................................................................................................. 58

4.1.1 Thermo-physical characterization ...................................................................... 58

4.1.2 Mechanical characterization ............................................................................... 65

4.2 MG-6403-Fc .............................................................................................................. 70

4.2.1 Thermo-physical characterization ...................................................................... 70

4.2.2 Mechanical characterization ............................................................................... 76

5 Discussion ......................................................................................................................... 79

5.1 CFC: general aspects ................................................................................................. 79

5.2 CFC: comparison ....................................................................................................... 81

5.3 MoGR ........................................................................................................................ 84

6 Conclusions ...................................................................................................................... 87

Future works ......................................................................................................................... 89

Appendix .................................................................................................................................. 91

Working principle of a thermocouple ................................................................................... 92

Working principle of a LVDT .............................................................................................. 93

Working principles of a strain gauge .................................................................................... 94

Wheatstone bridge ................................................................................................................ 95

Working principle of a load cell ........................................................................................... 97

Uncertainty of a measurement .............................................................................................. 98

Type A uncertainty ........................................................................................................... 99

Type B uncertainty ......................................................................................................... 100

Combined standard uncertainty ...................................................................................... 101

References .............................................................................................................................. 103

Bibliography ........................................................................................................................... 106

List of figures ......................................................................................................................... 107

List of tables ........................................................................................................................... 111

INTRODUCTION

I

Introduction

This introductive chapter depicts the background of the R&D activities carried out by the

Mechanical and Material Engineering group of the Engineering department, aiming at the

development of novel materials for the upgrade of the LHC’s collimation system. The aim and

structure of the thesis are explained in the final paragraph.

Background

CERN: European Organization for Nuclear Research

After the Second World War, a small group of European physicists, inspired by the

establishment of several international organizations, dreamed about a European laboratory for

atomic physics aimed to unite the efforts of European scientists. Thanks to their vision, CERN

(Conseil Européen pour la Recherche Nucléaire) was founded in 1954 in Geneva, Switzerland

(see Figure 0.1), and today it counts 22 member states and leads what has become the largest

particle physics laboratory in the world. Here, everyday physicists and engineers work together

to find answers to some of the most ancient dilemmas that afflicted humanity: which are our

origins? What is the structure of the matter?

INTRODUCTION

II

These investigations are commonly carried out by means of particle accelerators, and at CERN

it is possible to accelerate particles with the highest-energy particle accelerator in the world, the

Large Hadron1 Collider (LHC).

Figure 0.1 Aerial view of the CERN site and accelerator complex.

CERN’s accelerator complex

The LHC is the last machine of a bigger complex (see Figure 0.2), consisting of a succession

of smaller linear and circular accelerators with increasingly higher energies. The whole system

is meant to prepare two counter-circulating proton (sometimes lead ions) beams starting from

the extraction of hydrogen atoms from a bottle. The protons are first injected in the Proton

Synchrotron Booster (PSB), and then sequentially in the Proton Synchrotron (PS) and Super

Proton Synchrotron (SPS), where they reach the energy of 450 GeV2. (1) This downstream

system of the LHC, also prepares the beam as a sequence of 2808 bunches, each one containing

1,1 ∙ 1011 protons, and injects them in the 27-km long LHC in two opposite directions

1 Hadrons are particles made of quarks, like protons and ions. 2 The electronvolt (eV) is the unit of measurement of energy generally used in particle physics. It represents the

energy of an electron accelerated by a potential difference of 1 V. In SI units: 1 𝑒𝑉 = 1,602 ∙ 10−19 𝐶 ∙ 1 𝑉 = 1,602 ∙ 10−19 𝐽.

INTRODUCTION

III

(clockwise and counter-clockwise). The collisions between the two beams occur within 4 main

experiments or detectors: CMS, ATLAS, ALICE and LHCb.

Figure 0.2 CERN’s accelerator complex. Credits CERN.

The LHC

In the LHC, sixteen (eight per beam) Radio Frequency accelerating cavities accelerate the

beams up to the energy of 7 TeV and their speed can reach 0.999999991 times the speed of

light in vacuum. In SI units, each beam stores an energy of 362 MJ (2808 𝑏𝑢𝑛𝑐ℎ𝑒𝑠 ∙ 1,1 ∙

1011 𝑝𝑟𝑜𝑡𝑜𝑛𝑠 ∙ 7 𝑇𝑒𝑉 = 362 𝑀𝐽), enough to melt 498,4 kg of copper. (2)

More than 1200 superconducting magnets (dipoles, quadrupoles, sextupoles, octupoles,

decapoles etc), operating between 1,9 K and 4,5 K, optimize the beams trajectories. Cryogenic

temperatures are necessary to guarantee the superconductivity of the coils. For example, in the

main dipoles, a temperature of 1,9 K (-271,3 ℃) permits to decrease the electrical resistance of

the niobium-titanium conductors allowing the circulation of 11.700 A of current and the

generation of 8,33 T magnetic field. (3)

INTRODUCTION

IV

The superconducting magnets are sensitive to any kind of heating: an increase of temperature

would lead to the passage from superconductivity to normal conductivity (magnet quench). The

passage of nominal current would not be allowed and the temperature would increase further

leading to catastrophic failure (as occurred during the accident of 2008).

During normal operation, a source of heating is represented by interactions between the magnets

and beam intercepting devices and the beam halo. Hence, it has been fundamental to foresee a

protective system, capable to reduce the beam losses and withstand the highest energetic

particle beam: the Collimation system.

The Collimation system

The collimation system consists of more than 100 collimators mainly placed in the 3rd and 7th

octant of the LHC (beam cleaning sections) and before and after the 4 main experiments (see

Figure 0.3).

Figure 0.3 Position of the collimators in the LHC.

The collimators are Beam Intercepting Devices (BID) designed to accomplish two main

functions:

• Beam cleaning: during normal operations, it is unavoidable to have beam losses, that

due to particles deviating from the ideal trajectory and impacting the surrounding

INTRODUCTION

V

components. As said, the interaction between these high energetic particles and the

magnets can lead to magnet quenches. Thanks to two parallel jaws (see Figure 0.6),

differently oriented in the collimators, which intercept the beam halo, only the core of

the beam is let free to circulate. Figure 0.4 shows how the interaction between the halo

and the primary collimator jaws origins a shower of secondary particles: for this reason,

the collimation systems has been realized with a multi-stage cleaning architecture,

relying on the properties of different jaws materials.

• Machine protection: this function is required in case of accident, when orbit errors

occur.

Figure 0.4 Interaction between beam halo and collimator jaws. Credits S. Redarelli. (4)

Among others, the following parameters influenced the design of the collimation system (see

Figure 0.6):

• Radio frequency impedance: the electromagnetic field of the beam generates an electron

cloud along the collimator, which interacts with the following beam and limit the LHC

from reaching its maximum energy. Therefore, it is important to have a good charge

evacuation (high electrical conductivity).

• Vacuum: the collimators environment is characterized by the ultra-high vacuum of the

LHC (10−13𝑎𝑡𝑚). This defines constraints regarding the outgassing rates and the

maximum operational temperature of the jaws.

• Dimensional stability: flatness (100 µm over 1 m), reproducibility of jaw settings and

knowledge of the collimator gap (<50 µm) are of paramount importance for the beam

cleaning and stability (see Figure 0.5).

INTRODUCTION

VI

• Maintenance and reliability: to allow safe working condition for the operators in case

of maintenance, the whole design and choice of the material properties should minimize

the dose rates.

Figure 0.5 Front view of the collimator jaws showing the aperture.

Figure 0.6 Assembly of a collimator and collimator blocks.

Aim and structure of the thesis

This work contains the scientific background and the results of the activities carried out during

a working period at the Mechanical measurement laboratory (EN-MME-EDM) of CERN as

Technical student. The scope of the job was to perform the thermo-physical and mechanical

characterization of novel materials, mainly aimed at the upgrade of the collimators, specifically

used for the jaws of the primary and secondary collimators. In fact, the upgrade of the current

collimators is necessary to face the higher beam energies foreseen by the HiLumi LHC. The

INTRODUCTION

VII

HL-LHC project targets an increment of the luminosity3 of the accelerator, increasing the

energy of the beam from 362 𝑀𝐽 to 692 𝑀𝐽 by 2020. The thermo-physical characterization was

carried out by means of a differential scanning calorimeter, a push-rod dilatometer and a laser

flash apparatus. The mechanical tests were performed with a universal testing machine and

impact excitation technique.

The first two chapters describe the state of the art of the materials object of the thesis (MoGR

and CFC), including a general overview of the figures of merit, and of the instruments and

techniques used for the measurements.

Chapter 3 represents the experimental part of the work and describes two of the materials tested

during the working period and the devices employed, with reference to the international

standards.

The results of the characterization campaign are shown in the fourth chapter and their analysis

is developed in the fifth one.

The final chapter concludes the work and outline the future developments following the

activities carried out.

3 One of the most important parameter of an accelerator is the luminosity, which indicates the number of collisions

that occur in a certain period. The higher the luminosity, the higher the number of collisions and therefore the

quantity of data and the probability to observe rare events. To increase the luminosity, it is possible to increase the

number of hadrons per bunch and/or to squeeze them in the smallest amount of space.

STATE OF THE ART: MATERIALS

1

1 State of the art: materials

The thesis work focuses on the thermo-physical and mechanical characterization of two

materials: carbon fibers - carbon (CFC FS140®) and molybdenum graphite (MoGR, MG-6403-

Fc), a molybdenum carbide - reinforced ceramic matrix composite (CMC). Both materials have

a graphitic ceramic matrix. The reinforcement, also ceramic, is provided by carbon fibers in the

CFC case and by molybdenum carbide in the MoGR. After introducing the Figures of Merit,

defined to evaluate the performances of the material when embarked in a collimator, the

predecessors of the two families of materials tested are described. In the final part, a full

overview of the materials currently employed in the collimators is depicted.

1.1 Figures of Merit

During the past years, several Figures of Merit (FoMs) have been defined to evaluate and rank

the candidate materials, taking into account the harsh environment and the requirements that

the collimators need to withstand. In a recent paper (5), four indexes relying on constant

temperature-independent material properties are proposed (for anisotropic materials the

averaged values in the three directions are considered):

• Thermomechanical robustness: this index assesses the material robustness against

particle beam impacts. When a particle hits a structure, it transfers instantaneously its

kinetic energy to the impacted body under the form of heat. Thermal shock problems


2

can then occur to the impacted material, which experiences a sudden temperature

change and induced thermal stresses and deformations. This index is based on both the

admissible strain, or strain to failure 휀𝑎𝑑𝑚, and the melting temperature 𝑇𝑚 of the

material:

TRI =εadm

휀𝑟𝑒𝑓∙ (

𝑇𝑚

∆𝑇𝑞− 1)

𝑚

1.1

Where 𝑚 is a coefficient related to the material softening with a temperature increase,

휀𝑟𝑒𝑓 and ∆𝑇𝑞 are the strain and the temperature increase generated by a reference beam

impact:

εadm =

𝑅𝑀

�� (1 − 𝜐) 1.2

εref = 𝛼 Δ𝑇𝑞 1.3

Δ𝑇𝑞 =

𝐶𝑅𝜌𝑛

𝑐𝑝𝑋𝑔 1.4

Where �� is the average Young’s modulus, 𝜐 the Poisson’s ratio, 𝛼 the average CTE, 𝑐𝑝

the specific heat, 𝑋𝑔 the geometric radiation length, 𝐶𝑅 a scaling factor and 𝑛 a constant

related to the energy distribution generated by the impact (empirically observed to be

~0.2). It is worth to notice in equation 1.4 that the energy deposited by the beam and

therefore the temperature rise, is directly proportional to the density.

• Thermal stability: this parameter gives an indication of the geometrical stability of the

material under steady-state particle losses. Differently from the TRI, the TSI is related

to an equilibrium scenario with the heat slowly deposited on the material and evacuated

through a cooling system. The TSI is therefore strongly related to the heat evacuation

capacity of the material, and therefore its thermal conductivity, and is proportional to

the radius of curvature of an elongated structure induced by a non-uniform temperature

distribution.


3

𝑇𝑆𝐼 =�� 𝑋𝑔

𝛼 𝐶𝑠 𝜌𝑛 1.5

where �� is the average thermal conductivity and 𝐶𝑠 a scaling factor.

• Electrical conductivity: this property must be maximized in the collimators to minimize

the Radio Frequency impedance (as explained in the Introduction). In fact, the

collimators are the devices closest to the beam and their contribution to the whole LHC

impedance is the highest.

• Radiation resistance: irradiation of materials by energetic particles causes

microstructural defects which translate into a degradation of the thermo-physical

properties. Radiation resistance is defined as the ability of the material to maintain its

properties under and after irradiation.

The FoMs are an efficient tool to quickly predict the behavior of a material when embarked in

a collimator. For a more precise estimation, however, the response of the material under the

particle beam is usually precisely evaluated by numerical methods, which makes use of material

models where the key thermo-physical and mechanical properties are expressed as a function

of the temperature. The properties required by the models were therefore extensively measured

during the characterization campaign detailed in this work.

1.2 Graphite

Graphite is a ceramic material and represents one of the allotropes of carbon. It is made of a

continuous stack of graphene planes, a structure where C atoms are arranged in a honeycomb

cell, forming covalent bonds with other three atoms. The graphene layers are bonded together

by weak Van der Waals forces, which for this reason can easily slide on top of each other. On

the other hand, it presents high strength, stiffness and low coefficient of thermal expansion

(CTE) in the planar direction, thanks to the covalent bonds. Despite being a ceramic material,

it shows good electrical conductivity along the graphene layers (higher than 2 𝑀𝑆/𝑚 for ideal

graphite along the basal plane). Graphite is the most stable form of carbon on Earth in standard

conditions. Commercial graphite has worse properties than the ideal crystal (Figure 1.1),

because it contains defects and it is polycrystalline.


4

Figure 1.1 Graphite structure (6).

Graphite occurs in nature in metamorphic and igneous rocks and it can be produced artificially

processing petroleum, coal or pitch coke. Artificial graphite production starts from raw material

that is ground up, bound and heated above its softening point. At this point, the material can be

variously shaped by extrusion, molding or isostatic pressing. The crystals are oriented

according to the process adopted. For examples, extrusion is chosen to produce carbon fibers.

The following step is the carbonization, which consists in the decomposition of organic

compounds into carbon through baking at 700 ÷ 1000 ℃ (with simultaneous elimination of

volatile components). The final phase is the graphitization, consisting in heating up to 3000 ℃

in an electric kiln for up to 3-weeks time: at this temperature, the carbon atoms are arranged in

the graphitic crystalline structure.

1.3 Ceramic matrix composites

This family of composites, produced by sintering technique, features a ceramic matrix and a

second ceramic phase as a reinforcement. The advantages of a ceramic matrix are: high

hardness, chemical stability, high melting temperature and thermal stability. On the other hand,

it confers low electrical conductivity and brittleness to the composite. For these reasons, they

are commonly used as small insert for cutting tools, while for collimator applications their

electrical conductivity is not high enough. The reinforcements are usually ceramics in form of

fibers, which add stiffness and strength. The main parameters to be defined in this family of

composites are the quantity of reinforcement, its shape, dimension and orientation, the quality

of the interface and the porosity.


5

1.4 Conventional reference system

Before dealing with the details of the collimators materials, it is important to introduce the

reference system conventionally adopted to refer to the collimator geometry, to the

manufacturing process, to the preparation of the samples and to the main direction of the

composites. The three directions are depicted in Figure 1.2.

Figure 1.2 Reference system adopted for collimator, manufacturing process and sampling.

• 𝑥: direction perpendicular to the plane of the jaw

• 𝑦: direction in the plane of the jaw, perpendicular to the beam

• 𝑧: direction in the plane of the jaw, parallel to the beam.

During the hot-pressing procedure, the pressure is applied in direction 𝑥.

The samples are cut along two directions: they have their axis either parallel to x (hereafter

identified by the index 𝑥) or in the plane yz (hereafter called 𝑦𝑧 samples).

1.5 Carbon fiber – Carbon composites

1.5.1 CFC fields of use

Reinforced carbon – carbon is appropriate for a wide range of high temperature applications

where a high thermal shock resistance, high thermal diffusivity and low CTE are required: a

famous example is its usage for the conical nose of the Space Shuttle. Since the 1970s it has


6

been adopted in the brake disks of Formula One cars. Other typical applications are in

electronics, in energy production (armor tiles of nuclear plants), and to build components of

heat treatment furnaces.

1.5.2 CFC AC150®

The CFC currently used in the collimators (AC150 manufactured by the Japanese Tatsuno4) is

a 2D composite with 40% carbon fibers randomly disposed in a graphite matrix to create several

layers parallel to the 𝑦𝑧 plane (see Figure 1.2). The jaws had been hot-rolled to confer slightly

different mechanical properties along the two planar directions, as shown in Table 1.1. The

resulting material is orthotropic with different properties along the pressing direction and along

the two perpendicular directions. It has been chosen in 2004 for the primary and secondary

collimators thanks to its low CTE and best compromise between low electrical resistivity and

high strength.

Property Unit Value

Density [g/cm3] 𝜌 = 1.885

Specific Heat [J/kgK] 𝑐𝑝 = 712

Young Modulus [GPa] 𝐸𝑥𝑥 = − 𝐸𝑦𝑦 = − 𝐸𝑧𝑧 = 62

Shear Modulus [GPa] 𝐺𝑥𝑦 = 2.16 𝐺𝑥𝑧 = 33 𝐺𝑦𝑧 = 33

Poisson’s Ratio [-] 𝜐 = 0.16

Flexural Strength [MPa] 𝑅𝐹𝑙,𝑥 = 10.3 𝑅𝐹𝑙,𝑦 = 104 𝑅𝐹𝑙,𝑧 = 139

Coefficient of Thermal Expansion [10-6 K-1] 𝛼𝑥 = 11 𝛼𝑦 = −0.8 𝛼𝑧 = −0.8

Thermal Conductivity [W/mK] 𝜆𝑥 = 54 𝜆𝑦 = 233 𝜆𝑧 = 304

Electrical Conductivity [MS/m] 𝜎𝑥 = 0.03 𝜎𝑦 = 0.18 𝜎𝑧 = 0.24

Table 1.1 CFC AC150® properties at room temperature along the three directions defined in 1.4.

The production of CFC follows a process similar to graphite, with the addition of the reinforcing

carbon fibers (Figure 1.3).

4 http://www.tatsunojapan.com/


7

Figure 1.3 Image of a pitch-derived carbon fiber.

1.6 Molybdenum carbide – Graphite composites

1.6.1 R&D

In recent years, a R&D program has been launched at CERN with the aim of developing novel

materials for the collimators: the requirements of these protective devices have become more

compelling in view of the upgrade of the LHC (HL-LHC) and, even more, of the proposed

construction of the FCC (Future Circular Collider5). For example, the CFC currently used in

the primary and secondary collimators might limit the full exploitation of the HL-LHC

potential, due to its high RF impedance induced by its very low electrical conductivity. The

novel materials shall optimize the combination of FoMs and efforts have been done to find a

compromise between the excellent properties of available graphitic materials, such as low

density, high thermal stability and low thermal expansion, and those typical of metals or

transition metal-based ceramics, such as high mechanical strength and high electrical

conductivity. CERN, partly within the EuCARD collaboration, involved several partners from

the academic, technology and industrial sectors and developed new advanced materials, among

which the most promising are:

5 The FCC, Future Circular Collider Study aims to reach collision energies of 100 TeV, by means of a 80-100 km

long accelerator. https://fcc.web.cern.ch/Pages/default.aspx

https://fcc.web.cern.ch/Pages/default.aspx


8

• Copper – Diamond (CuCD): it is a diamond-reinforced Metal Matrix Composite

(MMC) produced by Rapid Hot-Pressing (RHP) of copper with addition of synthetic

diamonds and boron (initial volume composition: 60% diamonds, 39% copper, 1%

boron). The resulting composite has very good thermal and electrical conductivity, and

the CTE is 0.33 ÷ 0.5 times that of pure copper. The disadvantages are the difficulties

in the machining, the high brittleness in respect to copper and the low melting point

(copper melts at 1084 ℃).

• Molybdenum Copper – Diamond (MoCuCD): this material was developed to improve

the mechanical strength of CuCD and decrease the CTE. This MMC is also obtained by

RHP technique, with the addition of Molybdenum as a third element. Despite the efforts,

the material presents good thermal conductivity and compaction but still brittle behavior

and slightly higher CTE.

• Molybdenum carbide – Graphite composite (MoGR): due to the high density and the

low melting point of Cu-based materials, the research focused on a family of graphitic

composites molybdenum carbide – based. Graphite shows a number of advantages over

diamond: it has lower density, it represents the most stable form of carbon, while

diamond is metastable and converts into graphite when heated, and it is less expensive.

Molybdenum carbide has been chosen because of its refractory nature with promising

properties up to 2000 ℃. More details about the development of this material are

included in the following paragraph.

1.6.2 MoGR

The first studies over metal carbide – graphite composites were carried out in the 1960s by

NASA (7): the molybdenum-graphite investigated had a brittle behavior and low mechanical

strength. In 2012, CERN established a cooperation with the Italian company BrevettiBizz6

(Verona, IT) to develop the production of this composite. Since then, several grades of MoGR

have been realized and tested. A broad range of parameters has been tested: composition,

powder types (spheroidal natural graphite flakes with or without addition of mesophase pitch-

derived carbon fibers), dimensions (average graphite flake diameter 45 µm, molybdenum

powder between 5 - 45 µm and carbon fibers in the range 250 µm – 3 mm) and processing

cycle.

6 http://www.brevettibizz.com/


9

Figure 1.4 SE image at high magnification of a graphite flake.

Production

The composite is produced by powder metallurgy technology, with the hot-pressing technique.

At the beginning of the material development, the solid phase sintering technique, based on the

diffusion of C atoms inside the Mo BCC lattice interstitial, was adopted, exploring a range of

temperatures below the melting point of the carbides. The technique has then been abandoned

because of the better results obtained with a liquid phase sintering. The first step in the

production is the preparation of the green body by compaction of the powders at room

temperature applying a pressure of 300 MPa.

Figure 1.5 Hot-pressing machine at BrevettiBizz.


10

The green body is then housed in a special graphite mold made by two punches and a jacket,

and the sintering cycles are performed thanks to a hot-pressing sintering machine (see Figure

1.5), which applies a pressure of 35 MPa and can reach temperatures higher than 2600 ℃ inside

the mold. The process is called Spark Plasma Sintering (SPS), also known as Field

Assisted Sintering Technique (FAST) or Pulsed Electric Current Sintering (PECS): the heat

generation is produced internally in the sintered material by the passage of a large electric

current, which induces energy losses by Joule effect. The sintering temperature is above the

eutectic Mo-C corresponding to a content of C of 45% and a temperature of 2589 ℃ (see Figure

1.6). The liquid phase allows a mechanism called catalytic graphitization by dissolution and

diffusion of carbon atoms, typical of Metal Carbide-Carbon composites (8) (6): C atoms

dissolve and diffuse in the liquid carbide and the graphite crystallites can grow and bond

between themselves. The applied uniaxial pressure orients the composite structure, which

results transversely isotropic: the graphite planes are oriented perpendicularly to the pressing

direction.

Figure 1.6 Molybdenum-Carbon phase diagram. The eutectic temperature MoC(1-x)-graphite is at 2857 K

(2584℃) (45 at% C)


11

During the melting of the carbides, part of the liquid phase spills out of the mold: being difficult

to quantify this amount, also the final porosity and the actual metal content are difficult to

calculate, they can be estimated a posteriori with microscopy analyses performed on the final

material. Another parameter which is difficult to determine is the temperature inside the mold:

in fact, the temperature during the sintering process is measured by means of a pyrometer

reading the temperature of the lower punch: however, it is possible to know that the eutectic

point is reached and melting occurs because of the abrupt change in height (change of density)

of the plates. The sintered plate (see Figure 1.7) is extracted from the molds and submitted to a

pressure-less heat treatment in order to release its internal stresses. The composition and

production parameters of two MoGR grades are presented in Table 1.2, while their properties

are reported in Table 1.3.

Figure 1.7 MoGR sintered plate.

Parameter Unit MG-6403-Ga MG-6541-Aa

S PS S PS

Estimated T [℃] 2600 2100 2600 2100 Time [s] 1200 3000 1200 3000 Pressure [MPa] 35 0 35 0 Atmosphere 10−1 𝑚𝑏𝑎𝑟 𝑁2 + 𝐻2 10−1 𝑚𝑏𝑎𝑟 𝑁2 + 𝐻2 Vol. Mo [%] 4.5 4.3 Vol. GR [%] 95.3 90.9 Vol. CF [%] 0 4.75 Vol. Ti [%] 0.2 0.05

Table 1.2 Process and composition parameter for two different grades of MoGR. S = sintering, PS = post

sintering phases.

The graphite powder used is a crystalline powder graphite with spheroidal flakes provided by

Asbury Carbons Company. The average particle size is 45 µm and at least 90% of the particles


12

ranges between 20 and 80 µm. Molybdenum and titanium particles are in average 5 µm and the

purity of the powder is above 99.9%. Titanium is added as phase stabilizer dopant.

1.7 Current collimator materials

Besides the already described CFC, the other materials currently embarked in the collimator

jaws are:

• Tungsten heavy alloy (Inermet180): it is obtained by liquid phase sintering of powders

(95% W, 3.5% Ni and 1.5% Cu in weight). The Ni-Cu phase melts and infiltrates the

voids between W grains. It is used in the tertiary collimator jaws and exhibits good

thermal and mechanical properties combined with a high density: for these reasons, it is

an efficient particles absorber.

• Dispersion-strengthened copper (Glidcop Al-15): its production is based on the powder

metallurgy. A fine dispersion of nano-metric alumina particles inside Cu grains is

realized, mixing together a pre-alloyed powder of Cu with small concentration of Al

and fine copper oxide powder. The mixture is compacted and cold worked by extrusion

to reduce Cu grain size. The alumina blocks the propagation of the dislocations

maintaining good mechanical properties at high temperatures (it is the Cu alloy which

presents the highest resistance to creep), whilst the thermal properties remain closed to

those of pure Cu. Glidcop was initially candidate for the HL-LHC secondary collimator

absorber, but its high density determined its rejection. Conversely, it is employed in the

jaw support bars (see Figure 0.6) because it maintains high yield stress after brazing and

because this component is not impacted by protons, therefore higher densities are not

problematic.

The properties of the materials described in this chapter are collected in the following Table

1.3.


13

Property Unit CFC

AC150®

Inermet180 GlidcopAl-

15 MG-6403-

Ga

MG-6541-

Aa

ROM yz x yz x

Density [g/cm3] 1.885 18 8.93 2.49 2.49

Melting

Temperature [℃] 3650 1400 1083 2589 2589

Specific Heat [J/kgK] 712 150 391 604 643

Elastic

Modulus [GPa] 62 360 130 65 4.1 73 4.7

CTE [10-6 K-1] 3.9 5.25 16.6 2.03 9.26 2.3 10

Thermal

Conductivity [W/mK] 197 90.5 365 547 56 507 45

Electrical

Conductivity [MS/m] 0.14 8.6 53.8 0.88 0.08 0.98 0.06

TRI [-] 1596 0.6 5.3 274 267

TSI [-] 54 0.1 0.8 43.3 37

Table 1.3 Tables of properties and FoMs at room temperature for the aforementioned materials. Note that while

for the MoGR grades the properties are given for the two direction of anisotropy, the values for CFC results from

the ROM (rule of mixtures) average. For CFC properties along its main direction see Table 1.1

STATE OF THE ART: METHODS

14

2 State of the art: methods

This Chapter introduces the thermo-physical and mechanical properties necessary to

characterize the materials candidate for the production of the primary and secondary collimators

jaws and to optimize the finite element models for simulations. After an overview of the

techniques developed for their measurements, those adopted by the Mechanical measurement

laboratory of CERN are described.

2.1 Thermo-physical properties and their measurement

2.1.1 Specific heat

The relationship between enthalpy, temperature and pressure for a substance can be written as:

𝑑ℎ = 𝑐𝑝𝑑𝑇 + 𝐵ℎ𝑑𝑝 2.1

Where

𝑐𝑝 = (𝑑ℎ

𝑑𝑇)

𝑝

𝐵ℎ = (𝑑𝑝

𝑑𝑇)

ℎ

2.2


15

𝑐𝑝 is a thermodynamic coefficient called specific heat at constant pressure. To understand its

meaning consider the case of a system free to expand subjected to a source of heat 𝑞 at constant

pressure (𝑑𝑝 = 0). In this case the variation of energy 𝑢 is:

𝑑𝑢 = 𝑑𝑞 − 𝑝𝑑𝑣 2.3

Where −𝑝𝑑𝑣 represents the work of dilatation (negative because done by the system on the

outside), 𝑑𝑣 being the variation of volume of the system. Remembering the definition of

enthalpy ℎ = 𝑢 + 𝑝𝑣 and substituting in equation 2.1:

𝑑𝑞 = 𝑐𝑝𝑑𝑇 2.4

Hence, 𝑐𝑝 can be read as the ratio between the heat inputted in a system and its change of

temperature. Its unit of measurement in SI units is 𝐽

𝑘𝑔𝐾, so an equivalent definition is that the

specific heat represents the amount of heat needed to increase the temperature of a unitary mass

of 1 degree Kelvin.

2.1.2 Methods for measuring the specific heat

The specific heat is usually measured with an instrument called calorimeter which is also able

to measure the heat of chemical reactions and phase changes. One of the first calorimeter used

to measure specific heat was Regnault’s calorimeter (Henry-Victor Regnault, 1810-1878)

composed by a dewar containing water and the examined substance: the water is mixed and its

temperature measured with a thermometer. The 𝑐𝑝 of the substance is calculated from the

variation of temperature of the water:

𝑚𝑤𝑐𝑝𝑤∆𝑇 = 𝑚𝑠𝑐𝑝𝑠∆𝑇

Many different types of calorimeter have been developed and the one of interest for this thesis

is based on the differential scanning calorimetry and is detailed in the following paragraph.

Another method to determine the specific heat is the laser flash technique, also used for

measuring the thermal diffusivity, and described in paragraph 2.1.6. The latter is a comparative

method which leads to reliable results only if the same amount of heat is provided to both a

reference sample and the unknown sample, condition which is hardly achieved.


16

Differential scanning calorimetry

When a sample is subjected to a linear temperature program, Equation 2.4 express how the heat

flow rate into the sample is directly proportional to the material specific heat. The principle of

the differential scanning calorimetry consists in measuring the heat flow of both the unknown

material and a reference sample to determine the specific heat as a function of temperature. In

a differential scanning calorimeter (DSC, see Figure 2.1), a sample holder containing two

symmetrical measuring cells is housed inside a furnace, and subjected to a linear temperature

program preceded and followed by isothermal steps (see Figure 2.2). Each of the measuring

cells hosts a closed pan: one of them is always empty while the other contains the sample

material. The measuring cells are fitted with thermocouples connected in series. Hence, the

output signal will be proportional to the difference of temperature of the measuring cells.

Figure 2.1 Schematic of a DSC. Credits NETZSCH.

Before measuring the standard and the unknown sample a baseline measurements is necessary

to establish the thermal capacity of the instrument itself: this is carried out with empty pans.

When the temperature starts increasing there may be an offset from the isothermal baseline due

to different thermal capacities of the two sample holders. Once the baseline is determined the

sample is placed in the pan and subjected exactly to the same temperature program: once again,

during the ramp there will be an offset from the isothermal signal due to the heat absorption of

the material. In Figure 2.2 the difference of area subtended for the materials and baseline offset

represents the change in heat content ∆𝑄 = ∫𝑑𝑞

𝑑𝑡𝑑𝑡

𝑡2

𝑡1.


17

Figure 2.2 Temperature program and calculation of 𝒄𝒑. (9)

The measurements of both the unknown material and of a standard with a well-known specific

heat (like sapphire or POCO-graphite) allows the determination of 𝑐𝑝 as follows:

𝑐𝑝

𝑐𝑝′

=𝑚′𝑦

𝑚𝑦′ 2.5

Where 𝑦 and 𝑦′ are the coordinate deflections for sample and standard respectively.

2.1.3 Coefficient of thermal expansion

All the materials change their dimension whenever a temperature change occurs: this fact is

fundamental in the design of components subjected to temperature changes, because the way

they react to temperature changes and the way they are constrained reflects on their state of

tension and deformation. The coefficient of thermal expansion expresses the expansion of the

material with temperature as the fractional increase in length per unit rise in temperature.


18

Figure 2.3 Length of the sample as a function of temperature.

Figure 2.3 shows the change in length of a material with the temperature. The coefficient of

thermal expansion can be variously defined, but the two most common expressions are:

• Average coefficient of thermal expansion (CTE): this parameter refers to a temperature

range measured starting from a reference temperature 𝑇0 that must be stated.

𝐶𝑇𝐸(𝑇) =

𝐿2 − 𝐿0

𝐿0

(𝑇2 − 𝑇0) =

1

𝐿0

∆𝐿

∆𝑇 2.6

Where 𝐿0 is the length at the reference temperature. This value can be seen as the slope

of the secant the points corresponding to 𝑇2 and 𝑇0 on the expansion curve.

• Thermal expansivity: this definition refers to a single temperature and is the slope of the

tangent to the curve of expansion in the point of interest. This is the limit of equation

2.6 when 𝑇2 and 𝑇0 come closer.

𝛼𝑡 =1

𝐿

𝑑𝐿

𝑑𝑇 2.7

The coefficient of thermal expansion is a temperature dependent property: typically increasing

with the temperature. Its SI unit is K-1: common values for metals and alloys are within 10 10−6

to 30 10−6 𝐾−1, while ceramics range from 1 10−6 to 20 10−6 𝐾−1.


19

2.1.4 Methods for measuring the coefficient of thermal expansion

To measure this property, it is needed to sense both the displacement and the temperature. The

displacement measurement can rely on several physical principles which are at the base of the

following, suitable for different situations:

• Mechanical dilatometry: the displacement of the sample resulting from the temperature

change is transmitted mechanically to a sensor, like a linear variable differential

transformer (LVDT). Typically, the displacement is transmitted by one or 2 rods (push-

rod dilatometers), that are in contact with the sample. The contact between the rod and

the sample is guaranteed by a tracking force, in the horizontal configuration, and by

their own weight in the vertical set-ups. The sample is embedded in a furnace, big

enough to produce a uniform heating along the specimen. During the measurements,

also the components of the instrument (rods and sample holder) are subjected to

heating/cooling and expand/contract accordingly: accurate results can only be obtained

if the material of the set-up is suitable. For temperatures up to 1000 ℃ (or lower

depending on affinity with the tested materials) vitreous silica is suggested. At higher

temperatures alumina and isotropic graphite are recommended: it is important that both

tube and rods are produced from the same batch of material with the same orientation.

The temperature can be measured with thermocouples of pyrometers.

• Optical method: the dimensional change in the samples is measured optically with

different techniques, that can be identified as follows:

o Optical imaging: this absolute technique of measurement is based on the

tracking of the spatial movement of images, which are targets of the samples,

such as its extremities, machined grooves, holes or indentation or pins attached.

The targets are viewed in a direction perpendicular to the displacement by

optical sensors. The illumination of the targets can be done from the front (image

created by the reflected light) or from the rear (image created by the profile).

Good results are obtained when the temperature is uniform between the targets

or when the gradient can be determined.

o Optical interference: this method measures the distance between 2 points in

terms of number of wavelengths travelling parallel to the direction of

displacement. It represents an absolute method if the sample chamber is under

vacuum, when there is no need for corrections for the change in refractive index


20

of the air with the temperature. An arrangement can be the one shown in Figure

2.4, where the sample S is placed in between two optical flats A and B.

Figure 2.4 Set-up for optical interferometers with the sample S in between two optical flats A and B. (10)

The flats’ distance change as the sample expands. A beam of monochromatic

light is reflected from the bottom surface of A (transparent) and from the top

surface of B. The two reflected rays interfere constructively or destructively

according on the distance x. At high temperatures, there are effects that must be

considered like the emitted light from the specimen and the deterioration of the

optical reflective surface with the time.

o Speckle pattern interferometry: the speckle effect is a particular interference

effect that occurs when two coherent and collimated laser beams are directed

onto a surface. This pattern change when the surface illuminated is deformed.

• Diffraction technique: the sample is in the form of powder, rotating crystal or

polycrystalline wire and enclosed in a suitable furnace. Monochromatic x-rays are

directed on the specimen and part of them is reflected with different angles. Using

Bragg’s relation, the distance between crystal planes can be calculated. This technique

is advantageous for measuring weak materials. Noteworthy that not always the

measurement of the expansion of the lattice corresponds to the bulk CTE (for example

when there is more than one phase).

Mechanical push-rod dilatometer scheme

The method adopted in this work is the mechanical dilatometry through the horizontal push-

rod dilatometer, whose main components are shown in Figure 2.5. The sample is kept in place


21

by the sample holder in the homogeneous temperature zone of the furnace. The temperature of

both the sample and the furnace are monitored through thermocouples. One of the push-rod

extremities is always in contact with the sample (the contact is guaranteed by a spring), while

the other one is connected to the linear variable displacement transducer (LVDT).

Figure 2.5 Scheme of a horizontal push-rod dilatometer.

As already mentioned, all the materials in the furnace expand, therefore the sensed length

variation is the contribution of sample, sample holder and pushrod change in length. To obtain

the data of the sample is necessary to calibrate the instrument, typically measuring a reference

material. A calibration constant can be evaluated as:

𝐴𝑇𝑖 = [(∆𝐿

𝐿0)

𝑡

− (∆𝐿

𝐿0)

𝑚

]𝑇𝑖

2.8

where the index 𝑇𝑖 refers to a general temperature at which the length is 𝐿𝑖, 𝑡 and 𝑚 refer to

the certified and the measured expansion of the reference material, respectively. The measured

expansion of the sample can then be corrected with the calibration constant as follow:

[∆𝐿

𝐿0]

𝑇𝑖

= [(∆𝐿

𝐿0)

𝑚

+ 𝐴]𝑇𝑖

2.9

The linear expansion of the test specimen is then used for the calculation of its coefficient of

thermal expansion:

[𝐶𝑇𝐸]𝑇𝑖 = [1

∆𝑇

∆𝐿

𝐿0 ]

𝑇𝑖

2.10


22

2.1.5 Energy balance equation, thermal conductivity and thermal

diffusivity

A physical property of a system is an extensive quantity if its value depends on the dimension

of the system itself: its magnitude results from the sum of the values of the same quantity for

the subsystems. Examples of extensive quantity are: volume, mass, energy and entropy. The

properties which are size-independent are intensive quantities, such as: pressure, density and

temperature. A system can be represented by the fluid contained in a volume 𝑉(𝑡) confined by

a closed surface 𝑆(𝑡), variable with the time 𝑡. The general extensive quantity (mass dependent)

can be expressed as a function of time and position 𝑟, 𝑐(𝑟, 𝑡). It is possible to express the

variation during the time of this property through the balance equation as follows:

𝑑

𝑑𝑡∭ 𝜌𝑐 𝑑𝑉

𝑉

= − ∯ 𝜌𝑐(𝑣 − ��𝑆)�� 𝑑𝑆

𝑆

+ ∯ 𝐽 ∙ �� 𝑑𝑆

𝑆

+ ∭ 𝜌𝛷 𝑑𝑉

𝑉

2.11

where �� is the speed of the fluid, ��𝑠 the speed of the surface, �� the external versor of the surface,

𝐽 the flux of the quantity 𝑐 through the surface per unit area and time, and 𝛷 represents the

sources/sink of 𝑐 per unit mass inside the system. It is worth to identify the global meaning of

each term of this equation. The term at the left is clearly the variation with the time of the

extensive quantity. This variation is given by a convective term (quantity of 𝑐 inputted/removed

from the system by the incoming/outgoing mass) plus a term of flux of 𝑐 through the surface

of the system, plus a term of generation/destruction of 𝑐 inside the system.

It is possible to write the energy balance of a system substituting to 𝑐 the total energy of the

system, given by the sum of the internal energy and the kinetic energy:

𝑢0 = 𝑢 +𝑣2

2 2.12

In this case the flux of energy is the heat flux 𝐽 = ��′′ [W/m2], 𝛷 is the generation/distruction of

heat 𝑞′′′ and in the hypothesis of homogeneity, isotropy and constant volume, 2.11 becomes:

𝑑

𝑑𝑡∭ 𝜌𝑢 𝑑𝑉

𝑉

= − ∯ 𝑞′′ ∙ �� 𝑑𝑆

𝑆

+ ∭ 𝑞′′′ 𝑑𝑉

𝑉

2.13


23

Thanks to Green’s theorem it is possible to rewrite the surface integral and express everything

with integrals on the volume:

𝑑

𝑑𝑡∭ 𝜌𝑢 𝑑𝑉

𝑉

= − ∭ 𝑑𝑖𝑣𝑞′′′ 𝑑𝑉

𝑉

+ ∭ 𝑞′′′ 𝑑𝑉

𝑉

2.14

Being the volume arbitrary this leads to:

𝜌𝜕𝑢

𝜕𝑡= −𝑑𝑖𝑣��′′ + 𝑞′′′ 2.15

The heat flux is defined by Fourier’s postulate:

��′′ = −𝜆𝑔𝑟𝑎𝑑𝑇 2.16

where the proportionality constant 𝜆 [W/mK] is called thermal conductivity and it is a physical

property of the substance. The meaning of this postulate is that the heat flows in the direction

opposite to the temperature gradient, hence from “hotter to colder” system’s regions. For a solid

the variation of energy can be expressed as:

𝑑𝑢 = 𝑐𝑝𝑑𝑇 → 𝜕𝑢

𝜕𝑡= 𝑐𝑝

𝜕𝑇

𝜕𝑡 2.17

Substituting equations 2.16 and 2.17 in equation 2.15 we obtain the so-called Fourier’s equation

or the thermal conductivity equation:

𝜌𝑐𝑝

𝜕𝑇

𝜕𝑡= 𝑑𝑖𝑣(𝜆𝑔𝑟𝑎𝑑𝑇) + 𝑞′′′ 2.18

which can be written also:

𝜕𝑇

𝜕𝑡=

𝜆(𝑇)

𝜌(𝑇)𝑐𝑝(𝑇)∇2𝑇 +

𝑞′′′

𝜌(𝑇)𝑐𝑝(𝑇) 2.19

At this point it is possible to define the thermal diffusivity as:

𝑎(𝑇) =𝜆(𝑇)

𝜌(𝑇)𝑐𝑝(𝑇) 2.20


24

[m2/s], which expresses how fast the heat propagates in the material. Figure 2.6 shows an

overview of the values of thermal conductivity for various materials: low conductive materials

are called insulating.

Figure 2.6 Indicative thermal conductivity values at room temperature [W/mK]. Credits NETZSCH.

2.1.6 Methods for measuring thermal conductivity

Most of the methods for measuring the thermal conductivity are direct, in the sense that they

aim at the measurement of this quantity reproducing thermal situations in the material that allow

the use of the Fourier’s postulate. Among these methods there are:

• Direct heating: an electrical current is circulated through the sample which heats up by

Joule heating. The measured voltage drop and temperature difference relate to the

thermal conductivity and electrical resistivity. The application of this method is limited

to electrically conductive materials.

• Comparative method: it is based on the comparison of temperature gradients. A sample

of the unknown material is sandwiched between two reference samples whose extremity

faces are at different temperatures. Measuring the temperature gradient of the 3 samples

and knowing that the heat flux through thermal resistances in series is the same, it is


25

possible to calculate the unknown thermal conductivity. This method is very simple, but

characterized by high uncertainties.

• Guarded heat flow meter method: it is similar to the previous method where instead of

references a flux gauge is used to determine the heat flux and the sample is placed

between a hot and a cold surface.

• Hot wire method: this method is suitable for thermal insulating materials. An electrical

conductive wire is embedded in the sample: for example, if the sample is a cylinder the

hot wire would be placed along its axis. When an electrical current flows in the wire, it

heats up and can be considered a linear heat source for the sample. The temperature rise

in the cylinder, which is inversely proportional to the square radius, is measured and the

thermal conductivity calculated.

These methods have some disadvantages like the surface heat losses, the thermal contact

resistance between the sample and its heat sinks/sources, besides large sample sizes and

length of time required. Moreover, they can be used in a relative short range of temperature.

The method of the laser flash is an indirect method for measuring the thermal conductivity,

measuring the thermal diffusivity instead. It is characterized by lower uncertainties and the

highest range of temperature (see Figure 2.7). Its functioning principle is described in the

following paragraph.

Figure 2.7 Operative ranges of different measurements method for thermal conductivity. Credits NETZSCH.


26

Theory and proceedings of the flash method

For all the disadvantages stated in 2.1.6 a flash method for determining thermal diffusivity had

been developed and described for the first time in 1960 by Parker et al. (11). With this method

some of the previous problems are solved: there is no thermal contact resistance because the

heat source is a flash lamp and the heat losses are minimized by making the measurement in a

very short time, during which the cooling can be neglected. The theory of the method is based

on the study of Carslaw and Jaeger about the conduction of heat in solids. They solved equation

2.19, in the case of adiabatic conditions and unidimensional problem, for a solid of uniform

thickness 𝐿:

𝑇(𝑥, 𝑡) =1

𝐿∫ 𝑇(𝑥, 0)𝑑𝑥

𝐿

0

+2

𝐿∑ 𝑒

(−𝑛2𝜋2𝑎𝑡

𝐿2 )∞

𝑛=1

∙ cos (𝑛𝜋𝑥

𝐿) ∫ 𝑇(𝑥, 0) cos (

𝑛𝜋𝑥

𝐿) 𝑑𝑥

𝐿

0

2.21

When a pulse of energy 𝑄 is instantaneously and uniformly absorbed in a small gap 𝑔 at the

front surface of the solid the temperature distribution in this moment is:

{𝑇(𝑥, 0) =

𝑄

𝜌𝑐𝑝𝑔 𝑓𝑜𝑟 0 < 𝑥 < 𝑔

𝑇(𝑥, 0) = 0 𝑓𝑜𝑟 𝑔 < 𝑥 < 𝐿

2.22

Therefore, the temperature history at rear face of the solid can be written from equation 2.21

with the initial conditions 2.22:

𝑇(𝐿, 𝑡) =𝑄

𝜌𝑐𝑝𝑔[1 + 2 ∑ (−1)𝑛𝑒

(−𝑛2𝜋2𝑎𝑡

𝐿2 )∞

𝑛=1] 2.23

It is possible to define the following dimensionless parameters:

𝑉(𝐿, 𝑡) =𝑇(𝐿, 𝑡)

𝑇𝑀 2.24

𝜔 =𝜋2𝑎𝑡

𝐿2 2.25

where 𝑇𝑀 is the maximum temperature reached by the rear face. Equation 2.26 correlates these

two terms which are plotted in Figure 2.8:


27

𝑉 = 1 + 2 ∑ (−1)𝑛𝑒(−𝑛2𝜔)∞

𝑛=1 2.26

Figure 2.8 Dimensionless plot of the rear surface. (11)

Thanks to this relationship it is possible to determine an expression for the thermal diffusivity

𝑎. When 𝑉 = 0.5, 𝜔 = 1.38 hence:

𝑎 =1.38𝐿2

𝜋2𝑡0.5= 0.1388

𝐿2

𝑡0.5 2.27

𝑡0.5 is the time necessary to the rear face to reach half of its maximum temperature. Knowing

the amount of energy 𝑄 absorbed by the front face it is possible to evaluate the specific heat of

the material with the relationship 𝑐𝑝𝜌 =𝑄

𝐿𝑇𝑀. The first set-up was composed of a commercially

available flash tube able to dissipate 400 J at each flash. The sample was blackened with

camphor black to maximize the energy absorption and the sample holder was also opaque to

avoid irradiation of the sample. The temperature at the rear face of the sample was measured

with a thermocouple and its output voltage was presented on an oscilloscope and photographed

with a Polaroid land camera. The method had an important success presenting some relevant

advantages: simple equipment, small specimen size, possibility to measure at high and low

temperatures by pre-heating or pre-cooling the system. After the first experiment and

publication, the method had been developed by modelling the system under less ideal boundary

conditions. Different scientists contributed in optimizing the model, among which:


28

• Cowan (12): he considered the heat losses due to convection and radiation at both front

and rear surfaces for a finite square impulse. He expressed dimensionless solutions for

different heat losses, concluding that the measurement of thermal diffusivity by pulse

method should give reliable results also when the heat losses cause a reduction of the

maximum temperature of the rear face of 80-90% the no-losses value.

• Cape and Lehman (13): they brought important improvements to the initial theory,

considering both heat losses due to radiation and finite pulse-time effects. The former

effect is considered by solving the thermal energy balance (equation 2.19) for a cylinder

sample of radius 𝑟0, with boundary conditions deriving from the Stefan-Boltzmann

radiation law for grey bodies:

𝑞 = 𝜎𝜖(𝑇4 − 𝑇0

4) 2.28

Where 𝜎 = 5.67 10−8 𝑊

𝑚2𝐾4 is the Stefan-Boltzmann constant, 𝜖 is the emissivity

(between 0 and 1 for grey bodies), 𝑇 the temperature of the sample and 𝑇0 the ambient

temperature. They expressed the temperature rise at the rear face (normalized to the

maximum temperature) in function of the time (normalized to the characteristic time

𝑡𝑐 = (𝐿

𝜋)

2 1

𝑎, that represents roughly the time needed to the heat pulse to propagate the

thickness of the sample) for different values of a dimensionless parameter dependent to

the radiation heat losses, 𝑌.

𝑌 = 𝑌𝑥 + (𝐿

𝑟0)

2

𝑌𝑟 2.29

𝑌𝑟 = 4𝜎휀𝑟𝑇0

3𝜆−1𝑟0 2.30

𝑌𝑥 = 4𝜎휀𝑥𝑇0

3𝜆−1𝐿 2.31

The solution is shown in Figure 2.9. We can distinguish two situations:

1. Low temperatures, Y<<1 (negligible radiation heat losses): in this case the solution

is equal to equation 2.27 derived by Parker et al., and the temperature rises from 𝑇0

to the constant final temperature 𝑇0 + 𝛿_𝑚𝑎𝑥 (see curve 1). For 𝑌 = 0, 𝑡

𝑡𝑐= 1.388.


29

2. High temperatures, 𝑌 <≅ 1 (see curves 2, 3 and 4): 𝑡

𝑡𝑐< 1.388 and the use of

equation 2.27 would lead in error. An iterative procedure must be applied to evaluate

𝑎: an initial value can be obtained with 2.27, and 𝑌 can be estimated with reasonable

values of emissivities. Using the corresponding curve one can obtain a new value

for 𝑎 and so on.

Figure 2.9 Normalized temperature rise of the rear face of the sample in function of time, for different heat

losses.

For 𝑌 < 5 10−2 the approximation of Parker et al., is accurate to about 5%.

The finite pulse time effect has been investigated for those cases when 𝜏, the pulse

duration, is comparable to the characteristic diffusion time 𝑡𝑐. In this situation, the rise

in temperature is expected to be retarded. In Figure 2.10 it is possible to observe that as

τ becomes closer to 𝑡𝑐 the coefficient of equation 2.27 increases, hence the correction is

in the opposite sense to the one applied to compensate for heat losses.


30

Figure 2.10 Normalized temperature rise at the back surface. Curve 1 is for 𝝉 = 𝟎. 𝟎𝟏 𝒕𝒄, curve 2 for 𝝉 = 𝟎. 𝟏 𝒕𝒄,

curve 3 for 𝝉 = 𝟎. 𝟓𝟏𝒕𝒄 and curve 4 for 𝝉 = 𝟎. 𝟗𝟏𝒕𝒄.

• Clark and Taylor (14): starting from the theoretical solution found by Cape and Lehman,

they developed the so-called ratio method, aimed to avoid the iterative procedure. With

the previous results, they plotted the ratio between 𝑡/𝑡𝑐 evaluated for 2 different percent

rise (eliminating 𝑡𝑐) which decrease with increasing heat loss and validated the method

testing a reference POCO-Graphite.

Laser flash apparatus scheme

The instrument of interest for this thesis and based on the flash method technique is the laser

flash apparatus, see Figure 2.11. The sample is placed on a tube-shaped sample holder

embedded in a furnace. The laser pulse is sent to the bottom (front) face of the sample by an

optical fiber and the temperature increase on the upper (rear) face is sensed by an infrared

detector. The furnace allows thermalize the test specimen at the desired temperature and to

measure the diffusivity corresponding at different temperatures. Both the temperature of the

sample surroundings and of the furnace are measured with thermocouples.


31

Figure 2.11 Scheme of a laser flash apparatus.

2.2 Mechanical properties and their measurement

2.2.1 Mechanical properties

When considering an isotropic homogeneous material, its elastic tensor is fully described with

two elastic properties, typically the Elastic Modulus E [GPa], the Poisson ratio ν [-] or the Shear

modulus [GPa]. The materials of interest of this work are anisotropic, meaning that they have

direction-dependent properties which are different in the direction parallel to the hot-pressing

direction and perpendicular to it. For this kind of materials, five properties are needed to define

the elastic tensor. The Young’s modulus can be expressed in two different ways (see Figure

2.12): we can imagine to cut the composite perpendicularly to the load application direction in

which case, to conserve the continuity of the matter, the deformation of the phases must be the

same for matrix and reinforcement (Voight assumption); if we rather cut the material parallel

to the load application the stresses on the phases must coincide to balance the force.


32

Figure 2.12 Scheme of Voigt and Reuss assumption for a reinforced composite.

𝐸𝑉 = 𝑓𝑣𝑚𝐸𝑚 + 𝑓𝑣𝑟𝐸𝑟 2.32

𝐸𝑅 = ( 𝑓𝑣𝑚

𝐸𝑚 +

𝑓𝑣𝑟

𝐸𝑟)

−1

2.33

Where the index 𝑣 indicates the volumetric fraction, 𝑚 the matrix and 𝑟 the reinforcement.

These two assumptions represent the upper and lower limit of the isotropic composite

respectively.

The materials tested are graphitic CMC reinforced with fibers or carbides, which have typically

a brittle behavior and limited plasticity. Non-ductile materials lack of any method of flowing

or yielding to accommodate the stresses applied, they basically don’t allow the movement of

dislocations. In this kind of material any flaw or crack (critical defect) can act as a stress

concentrator, giving rise to a tri-axial stress state of tension. As soon as the intensification of

the stress overcomes the material’s resistance, the highest stresses flaw tip propagates causing

the failure of the piece. Hence, in these kind of materials, the strength depends on the flaws,

usually smaller than 100 µm, which are difficult to eliminate and to see. This leads to a huge

scatter of the size of the critical defect and consequently to a huge scatter on the values

representative of the strength. As consequences: the strength cannot be determined until the test

piece breaks, it requires a large number of tests to have reliability on the average, there will be

always test pieces significantly weaker and stronger than the average.


33

2.2.2 Methods for measuring the mechanical properties

The most known method to determine the behavior of a material in its elastic range is the tensile

test, which consists in applying an increasing force along the axis of a beam-shaped specimen.

Both the load and the strain of the sample are recorded and depicted in the stress-strain curve

of the material: from these curves (see Figure 2.13), it is possible to extract information about

the material, such as ductile/fragile nature, Young’s modulus (slope of the linear section of the

stress-strain curve), strain to rupture, stress to rupture, resilience etc.

Figure 2.13 Stress-strain curves representing brittle and ductile behaviors.

Despite its advantages, this method is not suitable to characterize the test specimens available

during this work, too small (due to manufacturing reasons) and not keen to be clamped in the

tensile tool jaws. Moreover, it is difficult to identify a purely linear region where to evaluate

the slope. Therefore, two different techniques are applied for the characterization: flexural test

and impact excitation technique (IET). When possible, also compression tests are performed to

have a more complete overview of the material behavior.

Compression test

One of the main advantages of this technique is the test specimen’s geometry: the sample is a

cylinder with flat extremities which do not need to interface with any fixture. In fact, the second

big advantage of the technique is the simplicity of the compression tooling: the specimen is

placed between two rigid plates that approaching each other give rise to a state of tension of

simple compression (provided there is no friction between the sample’s basis and the plates).

The stress can be evaluated as follows:

𝜎𝑐 =𝐹

𝐴 2.34


34

Where 𝐹 is the compressive force and 𝐴 the cross sectional area of the specimen. The most

important quantities obtained from these tests are the stress and strain to rupture in compression.

Impact Excitation Technique

This dynamic method is a non-destructive technique widely used to characterize brittle

materials, such as ceramics, as it requires a small specimen of simple geometry and allows to

obtain Young’s modulus, Poisson ratio and Shear modulus with a single measurement and set-

up. On the other hand, it is sensitive to flaw in the geometry (machining damages, surface finish

and poor geometric tolerances). The sample is a beam test-piece with uniform cross-section and

the method relies on the fact that the vibration modes of the bodies are determined by their

mass, geometry and elastic properties. The modes are determined by measuring the vibration

of the test specimen when stricken by a hammer: the sample would “ring” and the sound

spectrum recorded to obtain the resonance frequencies (the method is also known as “Natural

frequencies method”). At the basis of the method there are the modes of vibration of the

prismatic beam, whose principal ones are:

- Flexural (out-of-plane and in-plane): depend on the Young’s modulus of the test-piece

in the longitudinal direction (roughly independent of the material anisotropy for a

slender beam). For a bar of isotropic and homogeneous material of mass 𝑚, length 𝑙,

width 𝑏 and thickness 𝑡, the Young’s modulus can be formulated as:

𝐸 = 0.9465 (𝑚𝑓𝑓

2

𝑏) (

𝐿3

𝑡3) 𝑇 2.35

Where the parameter 𝑇 is:

𝑇 = 1 + 6.585(1 + 0.0752𝜈 + 0.8109𝜈2) (𝑡

𝐿)

2

− 0.868 (𝑡

𝐿)

4

− [8.34 (1 + 0.2023𝜈 + 2.173𝜈2 (

𝑡𝐿)

4

)

1 + 6.338(1 + 0.1408𝜈 + 1.536𝜈2) (𝑡𝐿)

2] 2.36

If 𝐿/𝑡 > 20 the expression can be simplified as 𝑇 = 1 + 6.858(𝑡/𝐿)^2, eliminating the

need to know the Poisson’s ratio a priori. In a free-free prismatic beam the out-of-plane


35

modes of vibration present nodes (minimum vibration) and antinodes (maximum

vibration) along the length as depicted in Figure 2.14.

Figure 2.14 Out-of-plane vibration modes of a free-free beam: nodal lines.

The first vibration mode has nodes at 0.223 times the length from the extremities and

antinodes in the center and at the extremities. This resonant mode can be excited in a

constrained beam if this is supported at the nodes and excited (especially at the center

and the extremities which are the antinodes, see Figure 2.15.

Figure 2.15 Nodes and antinodes of the first out-of-plane flexural mode.

- Torsional: for isotropic materials, it depends on the shear modulus. For anisotropic

materials, it is controlled by a mix of shear stiffness in the principal planes. The shear

modulus is related to the fundamental torsional frequency through the relation:

𝐺 =4𝐿𝑚𝑓𝑡

2

𝑏𝑡[

𝐵

1 + 𝐴] 2.37


36

Where the shape term 𝐵 is:

𝐵 =

𝑏𝑡 +

𝑡𝑏

4 (𝑡𝑏

) − 2.52 (𝑡𝑏

)2

+ 0.21 (𝑡𝑏

)6

2.38

And the empirical correction factor 𝐴 is:

𝐴 =

0.5062 − 0.8776 (𝑏𝑡) + 0.3504 (

𝑏𝑡)

2

− 0.0078 (𝑏𝑡)

3

12.03 (𝑏𝑡) + 9.892 (

𝑏𝑡)

2

2.39

From Figure 2.16 and Figure 2.17 it is possible to see that to excite the first torsional

mode the beam must be supported at the center (node).

Figure 2.16 Torsional mode of a free-free prismatic beam: nodal lines.

Figure 2.17 Nodes and antinodes of the first torsional mode.


37

- Longitudinal: these modes of vibration, depend on the Young’s modulus and the

Poisson’s ratio in the longitudinal direction. They are associated to higher frequencies

(lower displacements) which are more difficult to be sensed by the available

instrumentation.

Looking at Figure 2.14 and Figure 2.16, it is clear how the nodal lines of the first flexural and

second torsional mode are similar: this suggests to use the same constraint configuration

employed to determine the first flexural mode also for determining the second torsional (which

ratio with the fundamental is 2:1). With one single set-up it is possible to determine E from the

fundamental flexural mode by striking the sample at the center, and G from the second torsional

mode by hitting it at the extremities (at a location off of the longitudinal nodal line). The

Poisson’s ratio can then be evaluated as:

𝜈 =𝐸

2𝐺− 1

The theory described in this paragraph is valid for isotropic materials, while those tested are

anisotropic: there exist more complex methods, which are actually used, to extract the elastic

properties of anisotropic materials from the sound spectrum recorded.

Flexural test

The flexural test consists in bending the bar-shaped test specimen, applying a force

perpendicular to its axis. While the force increases, the stresses inside the beam increase in an

elastic fashion (within the elastic range): those in the convex side of curvature are tensile

stresses while those in the concave side are compressive stresses, both directed along the axis

of the specimen. Compressive and tensile stresses have different effects on the behavior of

brittle materials: while the former tend to close the voids and cracks, the latter promote the

propagation of cracks. Therefore, when performing these tests the convex side of the specimen

in the vicinity of the surface (where the stress intensity is higher) is normally where the fracture

starts. The flexural test presents some advantages in comparison to the tensile test, such as: no

problems of gripping, easy alignment, cheap set-up, rapidity. Among the disadvantages there is

the tendency of superficial flaws to dominate the behavior.

There are two main set-ups available to perform flexural tests: the three-point and four-point

bending see Figure 2.18.


38

Figure 2.18 Support and load application in the 3- and 4-point bending.

The stress at fracture can be evaluated for a thin beam with rectangular section as follows:

𝜎𝑓3 =3𝐹𝑚𝑙

2𝑏ℎ2 2.40

𝜎𝑓4 =3𝐹𝑚𝑑1

𝑏ℎ2 2.41

Where 𝐹𝑚 is the maximum force applied, 𝑙 the support span, 𝑑1the distance between the inner

loading roller and the outer support, 𝑏 the width of the test piece and ℎ its thickness. The stresses

evaluated are called nominal flexural stresses because they refer to the outer fiber and may be

greater than the value which caused the fracture origin at the critical defect. Three-point bending

it is easier to perform while the four-point arrangement is normally preferred because a larger

volume of material is at the same level of nominal stress, resulting in a method which is more

searching for big defects. A consequence is that the ultimate stresses evaluated with the three-

point bending are generally higher. The Standards usually define the more appropriate method

or they allow both.

As described in the NPL guide No.98 (15), the flexural test can be performed as an alternative

method to the tensile test for the determination of the Young’s modulus. Using a thin beam tests

specimen, the calculation (Timoshenko theory) can be done measuring the deformation of the

outer fiber by measuring either the displacement or the net out-of-plane displacement of two

points of the sample surface or applying strain gages on the face of the specimen at the span

center. In the latter case, the one adopted during the tests, the expression of the Young’s

modulus becomes (4-point bending configuration):


39

𝐸 =3(𝐹2 − 𝐹1)𝑑1

𝑏ℎ2휀 2.42

Where 𝐹1 and 𝐹2 are the upper and lower level of forces selected from the recordings and 휀 the

corresponding measured strain.

EXPERIMENTAL WORK: MATERIALS AND METHODS

40

3 Experimental work:

materials and methods

3.1 Materials

In the framework of the R&D project on the collimators’ jaws materials, two different graphitic

composites are selected for the mechanical and thermo-physical characterization: CFC FS140®

and MG-6403-Fc. Both are candidates for the production of new primary and secondary

collimators.

3.1.1 CFC FS140®

This carbon fiber-carbon composite is manufactured by the Japanese Tatsuno, as the CFC

AC150® described in 1.5.2. Tatsuno’s CFC is the absorber material used on the low-density

collimators (primary and secondary) since 2004, due to its decent electrical conductivity and

high strength. During the development of the new TCPPs (primary collimators), this same CFC

was expected to be employed but since the first order the Asiatic manufacturer had changed the

provider of raw CF, from the AK-150 Across Co. to the FS140 CFC Design Co. Hence, a new

and complete thermo-physical and mechanical characterization is required. Many information

about this material are missing, since they have not been provided by the manufacturer, both

regarding the composition and the details of the production process. In general, the production


41

process of CFCs follows the one of graphite, explained in 1.2 , with the addition of carbon

fibers. The graphitization temperature is 2500 ℃, 300 ℃ less than the CFC AC150®.

The material was ordered in the shape of a plate of dimension 1230 𝑚𝑚 𝑥 500 𝑚𝑚 𝑥 27 𝑚𝑚.

The plate was then machined in the CERN’s workshop by conventional milling and turning to

obtain the samples listed in Table 3.1 and shown in Figure 3.1:

Test Dimension [mm] Direction Nr of samples

Dilatometry Φ 6 x 25 yz 6

x 6

Calorimetry Φ 5 x 0.75 - 6

LFA Φ 12.5 x 3 yz 6

x 6

Flexural test

(IET)

4 x 10 x 25 yz 6

x 6

Compression test Φ 7.5 x 15 yz 6

x 6

Electrical conductivity 4 x 4 x 30 yz 6

x 6 Table 3.1 List of CFC FS140® samples’ dimensions and cutting directions.

Figure 3.1 Picture of CFC FS140® test specimens for the thermo-physical (left) and mechanical (right)

characterization.

A class I hydrostatic balance is used to determine the density of the material, measuring the

LFA samples before the thermo-physical characterization. The averages of three measurements

over each of four samples are stated in Table 3.2:


42

Sample Density [g/cm3]

S1 1.851

S2 1.882

S3 1.875

S4 1.894 Table 3.2 Density (average of three consecutive measurements) of four CFC FS140® samples. The ambient

temperature was 23 ℃ and the density of the medium (ethanol) 0.787 g/cm3.

3.1.2 MG-6403-Fc

This grade of molybdenum carbide reinforced graphite is one of the multiple MoGR grades

produced within the collaboration with the Italian SME BrevettiBizz. Thanks to the

cooperation, many more details are available in terms of composition and production process.

Table 3.3 contains details about the composition, while the parameters of the production

process, which is described in 1.6.2, are depicted in Table 3.4.

Vol. % Mo 4.5

Vol. % graphite 95.3

Vol. % Ti 0.2 Table 3.3 Composition of MG-6403-Fc.

Process parameter S PS

Estimated temperature [℃] 2600 2600

Time [s] 1200 3000

Pressure on the plate [MPa] 35 0

Atmosphere 10-3 mbar - air Table 3.4 Production process parameters. S=sintering, PS= post sintering.

The dimensions of the plate after sintering and post-sintering treatment are

150 𝑚𝑚 𝑥 100 𝑚𝑚 𝑥 26.5 𝑚𝑚. The samples are cut by traditional milling and turning at the

BrevettiBizz facility, in the number and dimensions stated in Table 3.5:

Test Dimension [mm] Direction Nr of samples

Dilatometry Φ 6 x 10 yz 3

x 3

Calorimetry Φ 5 x 0.75 - 3

LFA Φ 10 x 2 yz 2

x 4

Flexural test

(IET, Electrical conductivity)

5 x 10 x 55 yz 5

5 x 10 x 25 x 4 Table 3.5 List of MG-6403-Fc samples’ dimensions and cutting directions.


43

The density of the material has been measured with a hydrostatic balance, and the averages of

three measurements done over two samples are in Table 3.6:

Sample Density [g/cm3]

S1 2.583

S2 2.589 Table 3.6 Density (average of three consecutive measurements) of two MG-6403-Fc samples. The room

temperature was 24 ℃ and the density of the medium (ethanol) 0.791 g/cm3.

Figure 3.2 shows a SEM image of a MG-6403-Fc sample cut along the x direction where it is

possible to see the basal planes of the graphitic matrix and the molybdenum carbides here

dispersed.

Figure 3.2 SEM image of MG-6403-Fc sample cut along the x direction.

3.2 Instruments for the thermo-physical analysis

In this section, the three instruments used for the thermo-physical characterization are

described. The claimed uncertainties of measurement are evaluated as explained in Appendix.

3.2.1 Push-rod dilatometer: DIL 402 E

The method used to measure the coefficient of thermal expansion is the mechanical dilatometry

through the horizontal push-rod dilatometer DIL 402 E made by NETZSCH, whose schematic

functioning is described in 2.1.4. The instrument has been produced with state of the art

technology and the standard test method ASTM E228, described below, is applicable.


44

Figure 3.3 DIL 402 E by NETZSCH and its scheme.

The electrical furnace is made of graphite and can reach 2000 ℃, it is suitable to operate both

under vacuum and in inert atmosphere. It is water cooled and its temperature is controlled by a

W3%Re-W25%Re thermocouple. A safety system always monitors both the flow of cooling

water and gas. Two set-ups of sample holder and push-rod are available: POCO-Graphite and

Al2O3 (for use in oxidizing atmosphere up to 1680 ℃). The sample, ideally in the shape of a

cylinder, is positioned inside the sample holder (see Figure 3.4) and the push-rod is approached

operating a micrometer screw. The temperature in its surroundings is measured with the same

type of thermocouple employed for the furnace. The LVDT is placed far from the measuring

zone and is thermalized by a distilled-water closed circuit.

Figure 3.4 Sample of POCO-Graphite housed in the sample holder with the Alumina set-up.


45

Some key technical data of the instrument are collected in Table 3.7:

Technical data

Temperature range RT-2000 ℃ Graphite set-up

RT-1680 ℃ Alumina set-up

Heating rate 0.01-50 K/min

Atmosphere

Inert (Ar, He > 2000 ℃)

Oxidizing (Alumina set-up)

Reducing

Static and dynamic

Vacuum 10-2 Pa

Measuring range 500-5000 µm

Load at the sample 15-45 10-2 N

ΔL resolution 0.125 nm/digit, 1.25 nm/digit

Other functionalities

Melting temperatures

Glass transitions and softening points meas.

Sintering temperature analysis

Sample containers for paste, liquid and

molten metals

Uncertainty (thermal expansion) ± 3.8%

Uncertainty (CTE) ± 5.3% Table 3.7 Key technical data of DIL 402 E.

The test parameters are listed in Table 3.8:

Instrument set-up Graphite

Atmosphere He 100 ml/min

Temperature

program

Isothermal step 10 min at 25 ℃

Heating phase 5 K/min up to 1950 ℃

Cooling phase 5 K/min down to 25 ℃


Reference material CFC FS140® POCO-graphite 24.998 mm

POCO-graphite 15.001 mm MG-6403-Fc Table 3.8 Dilatometry test set-up.

ASTM E228: Standard test method for linear thermal expansion of solid

materials with a push-rod dilatometer (16)

The test method aims to reduce the variability of the test conditions in order to realize

measurements which are comparable and to minimize the arbitrariness of the test. The Standard

describes the calibration method, apparatus, procedure, preparation of the tests specimen and

calculation of the quantities of interest. Some of the most important recommendation and good

practices are:


46

• Apparatus:

o the sample holder and push-rod should come from the same material,

uncontrolled substitutions lead to increase of uncertainties. A general

verification can be done measuring a specimen cut from the same material: its

CTE should be smaller than ±0.3 10-6 K-1.

o The temperature control of the furnace at a constant rate should be monotonous

within ±2℃ (or 5% of the instrument’s maximum temperature), while the

control of equilibrium shall be within ±1℃ (or ±0.05% of the instrument

maximum temperature).

o The displacement transducer must cover the expected displacement within its

linear range. Its resolution must be not less than 0.1% of its linear range and a

linearity of at least ±0.1% of their linear range.

o The specimen temperature must be sensed with calibrated sensor capable to

provide indication of this temperature ±0.5℃ (or ±0.1% of its overall

temperature range). The position of the sample thermocouple is important: a

good practice is to place the head of the thermocouple equidistant from the

specimen and the sample holder, and shielded from the direct view of the heating

element.

• Test specimen: the specimen should be between 25 and 60 mm long and between 5 and

10 mm in diameter (or equivalent if not cylindrical). Its cross sections must be robust to

prevent buckling or creep and its ends must be smooth, parallel and it should form point

contact with the dilatometer. Determine the initial and final length of the sample with a

measuring tool capable of reading to at least 25 µm.

• Procedure: measure the initial length of the specimen and place it in the sample holder

making sure it is stable. The measurement of CTE can be done either heating (cooling)

the specimen to incremental constant temperatures hold until the transducer reads

variations less than ±2µm, or heating (cooling) at a constant rate equal or lower than

5℃/min. In the former case the mean temperature of the specimen may differ from the

measured temperature, but the measured expansion is accurate if the calibration is done

correctly.


47

3.2.2 Laser flash apparatus: LFA 427

The instrument used to measure the thermal diffusivity is the Laser flash apparatus LFA 427

by NETZSCH, see Figure 3.5. The instrument has been produced with state of the art

technology and the standard test method ASTM E2585, is applicable.

Figure 3.5 LFA 427 by NETZSCH with control cabinet, data acquisition system and laser source and scheme of

the measuring part.

The electric furnace is capable to reach 2000 ℃ and it is made of a heating element ad insulation

made of graphite and mounted in a water-cooled housing. The top and the bottom of the furnace

are sealed with a calcium fluoride and fused silica lenses respectively. The measurements can

be done under vacuum, in inert atmosphere and oxidizing atmosphere (alumina set-up). The

vertical set-up allows an easy handling of the sample which is housed in a tube-shaped sample

holder, where it lies on three tiny supports to minimize the conductive heat losses. A cap is

placed on the sample to avoid direct illuminate the detector and reduce signal disturbance, see

Figure 3.6.


48

Figure 3.6 Sample holder and cap.

The optical fiber extremity is embedded in the bottom part of the device and targets the front

face of the sample through the fused silica window. The IR detector (indium antimonide) is

mounted directly on the top of the furnace, it has a visual contact with the upper face of the test

specimen and it is nitrogen liquid cooled.

Some key technical data are listed in Table 3.9.

Technical data

Temperature range RT-2000 ℃

Diffusivity range 0.01-1000 mm2/s

Standard sample dimensions 0.1-6 mm thick

6-12.7 mm diameter

Atmosphere

vacuum: 10-5 bar

static /dynamic inert gas (Ar, He)

oxidizing atmosphere

Laser

Nd: YAG

Power max: 25 J/pulse

Pulse width: 0.3-1.2 ms

Wave length: 1064 nm

IR detector InSb

Other functionalities

Thermal contact resistance

Lamellar samples

In-plane measurements

Powder and liquid samples

Specific heat evaluation

Measurement with mechanical pressure

Square samples

Uncertainty (thermal diffusivity) ± 5.6% Table 3.9 Key technical data of LFA 427 by NETZSCH.


49


Instrument set-up Graphite

Atmosphere Ar 100 ml/min

Laser voltage 550 V

Pulse duration 0.6 ms

Temperature program 20-1950 ℃ divided in 20 isothermal steps

5 shots at every isothermal step

Model for calculation Cape-Lehman + pulse correction Table 3.10 Laser flash test set-up.

ASTM E2585: Standard practice for Thermal diffusivity by the Flash

Method (17)

This practice contains some details regarding the measurement of the thermal diffusivity of

primarily homogeneous isotropic and solid materials within 10-7 - 10-3 m2/s, ranging from 75 to

2800 K. The flash method is an absolute technique, reference materials can be used to verify its

performances though. This method has been shown to produce useful data also for anisotropic

materials, provided that the directional thermal diffusivities are mutually orthogonal and the

heat flow produced is unidirectional. A number of international round robin testing programs

have shown that a measurement precision of 5% can be attained for thermal diffusivity. The

standard describes the apparatus, procedure, preparation of the tests specimen and calculation

of the quantities of interest. Some of the most important recommendation and good practices

are:

• Apparatus:

o The duration of the flash should be less than 2% of the half time rise to keep

error due to finite pulse width less than 0.5%. The pulse intensity should be

spatially uniform. Since most of the lasers have higher intensity in the center the

spot should be larger than the specimen diameter. The uniformity is improved

up to 95% using an optical fiber.

o The furnace should keep the temperature constant within 4% of the maximum

temperature rise over a time period equal to five times the maximum time rise.

o The detector shall be capable to detect 0.05 K increase of temperature. The

response time must be smaller than 2% the half time rise. The view windows

must not absorb the radiation in the wavelength region of the detector, therefore

they have to be cleaned and kept free from deposits.


50

o The data acquisition system must have an adequate speed to have the time

resolution in determining half of the maximum temperature rise on the

thermogram at least 1%.

• Test specimen: the diameter usually varies between 10 to 12.7 mm. Smaller samples

provide lower energy at the rear face. The optimum thickness depends on the estimated

value of thermal diffusivity and should lead to maximum temperature time rises between

10 to 1000 ms. At high temperatures, smaller samples minimize the heat loss correction.

Typical thicknesses are 1-6 mm. A thickness cannot be optimal for both measurements

at low and high temperatures. The faces of the specimen must be flat within 0.5% their

thickness. Their surfaces should not be shiny, to avoid reflection of laser light on the

front face and to produce a strong signal on the rear one, it is common to apply a thin

coating layer of high emissivity material, such as graphite.

3.2.3 Differential scanning calorimeter: DSC Pegasus 404C

Figure 3.7 DSC Pegasus 404 C by NETZSCH and its schematic view.

The specific heat measurements are carried out with the differential scanning calorimetry DSC

Pegasus 404 C by NETZSCH. The rhodium furnace is air cooled and it allows to reach 1650

℃, it can operate under vacuum or inert atmosphere. The sample holder is a Pt/Rh sensor that

can host the two crucibles (as explained in 0) and senses the temperature of the test specimen

and the reference pan. Its position can be adjusted by means of two micrometric screws, to have

a uniform heating of the two crucibles. An oxygen trap system is also positioned on top of the

shielding plates of the sample holder: this small getter is useful to reduce the amount of oxygen

below 1 ppm (Figure 3.8).


51

Figure 3.8 Sample holder and OTS system.

Some key technical data are listed in Table 3.11.

Technical data

Temperature range RT-1650 ℃

Reproducibility <0.3 K for temperatures below 1000℃

Baseline reproducibility <±1 mW for T<1500℃

<±2.5 mW for T>1500℃

Uncertainty (specific heat) ± 3.5% Table 3.11 Technical data of the DSC Pegasus 404 C.


Instrument set-up Graphite crucibles + alumina washers

Atmosphere Ar 50 ml/min

Temperature

program


Heating phase 15 K/min up to 700 ℃

Isothermal step 20 min at 700 ℃ Table 3.12 Calorimetry test set-up.

DIN 51 007: General principles of differential thermal analysis (18)

This standard covers a variety of methods to analyze solid and liquid materials through the

differential scanning calorimetry like chemical reactions, glass transition temperatures, phase

transitions and specific heat capacity. It describes the concepts, apparatus, procedures, test

specimens and evaluation. Some of the most important recommendation and good practices are:

• Apparatus:

o The furnace shall be able to cover heating rates from 1 to 50 ℃/min.


52

o The temperature control should maintain a constant heating rate between

5℃/min and 50℃/min to an accuracy of 10%. In the isothermal steps the

temperature shall not deviate more than 0.5% from the target temperature. When

switching from a dynamic step to an isothermal program the damping in

temperature should be less than 20% of the numerical value of the heating rate

and the decay time should be less than 5 minutes.

o When the sample can react with air the test must be done under controlled

atmosphere (inert gas). The effect of the gas flow on the thermal measurement

must be minimum and its temperature shall reach the specimen temperature by

the time it reaches the specimen.

o The differential temperature shall be measured with a device that have a limit

error of no more than 0.5% and it should be able to sense temperature changes

of less than 1℃.

• Procedure for measuring specific heat:

o The measurement is carried out on one empty and one full specimen holder and

the temperature program begins with an isothermal step at the initial temperature

followed by a dynamic phase and ends with another isothermal step at the final

temperature.

3.3 Instruments for the mechanical characterization

3.3.1 Universal testing machine: Zwick/Roell Z400

The machine used to perform the mechanical tests is a universal testing machine tailor made

for the mechanical laboratory by Zwick/Roell (see Figure 3.9). It allows to perform tensile,

compressive and flexural tests and to host additional fixtures designed at CERN for specific

purposes.


53

Figure 3.9 Universal testing machine Zwick Z400.

Some of the key features of the machine are listed in Table 3.13:

Component Features

Machine 4 columns, electro-mechanical drive by two

ball screws, two test areas, test speed 0.001 ÷

250 mm/min, resolution crosshead motion

0.024 µm

High capacity load cells 400 kN

250 kN

Compression plates 55 HRC hardness

0.05 mm planarity

upper plate spherically mounted Table 3.13 Features of the universal testing machine Zwick Z400.

Compression test set-up

The compressive test set-up requires that the top plate sit on a top of a spherical bearing block.

The sample is simply positioned between the compression plates in the bottom part of the


54

machine. The co-axiality with the machine is checked visually and minimized to reduce the

effect of eccentric loading.

The test parameters adopted in the campaign are listed in Table 3.14:

Force sensor Zwick loadcell 250 kN

Strain sensor HBM strain gage 1-LY11-3/350

Crosshead motion rate 0.1 - 0.5 mm/min

Preload 20 N

Support span 20 mm

Loading span 10 mm Table 3.14 Compression test parameters.

ASTM C695: Standard test method for compressive strength of carbon and

graphite (19)

This test method claims some good practices regarding the apparatus, test specimen and

procedure regarding the determination of the compressive strength over carbon and graphite

products. The compression test provides a measure of the maximum loading capacity of these

materials, which typically support higher loads in compression. Among the recommendation:

• The test specimens should be cylinder with planar ends faces perpendicular to the

cylindrical surface to within 0.001 mm/mm of diameter. The edges should be sharp and

without flaws. The diameter should be greater than 10 times the maximum particle size.

The ratio height/diameter should range between 1.9 and 2.1.

• Regarding the positioning, the deviation of the specimen axis to the machine axis

should be within 5% of the sample diameter. The load should be applied continuously

at a constant rate of the crosshead displacement. The crosshead rate should lead to

breaking times higher than 30 s.

Flexural set-up

The 4-point bending test is performed with a dedicated fixture realized at CERN’s workshop,

which allow to adjust the loading and support spans and to change the interfacing components’

material. This results in a flexible tooling able to house specimens of various sizes and to

properly test materials with completely different mechanical properties (plastic, ceramics and

metals). The set-up used to test the specimens object of this work is shown in Figure 3.10: the

support blocks are made of steel AISI 304L, the rollers of tungsten carbide and their diameter

is 6 mm.


55

Figure 3.10 Fixture for the 4-point bending test.

Force sensor HBM load cell S2M 1000 N

Strain sensor HBM strain gage 1-LY11-3/350

Crosshead motion rate 0.1 mm/min

Preload 0 - 20 N Table 3.15 Bending test parameters.

ASTM C1161: Standard test method for flexural strength for advanced

ceramics at ambient temperature (20)

The standard provides indications regarding the preparation and execution of the flexural test

in both 3- and 4-point configuration over advanced ceramic materials. Some of the key aspects

are:

• Apparatus

o The loading should be done in any suitable machine capable to provide a

uniform rate. Its accuracy should be within 0.5%.

o The bearings of the fixture must be free to roll outward (support bearings) and

inward (loading bearings), to relieve frictional constraints.

• Specimen

o The test specimen has rectangular cross section of standardized dimensions and

its four longitudinal faces should be parallel within 0.015 mm.


56

o Carefully handle and store the test specimens to avoid introduction of random

flaws.

• Procedure

o The preload should be choses so that the corresponding stress don’t exceed 25%

of the mean strength.

o The crosshead rate should be chosen so that the strain rate in the sample is in the

order of 1*10-4 s-1. The strain rate is evaluated as ∈= 6𝑑𝑠/𝐿^2 where 𝑑 is the

thickness, 𝑠 the crosshead speed and 𝐿 the support span. The times to failure for

ceramics range between 3 and 30 s.

3.3.2 Impact excitation technique

IET set-up and devices

The set-up adopted to carry out the impact excitation technique is very simple and it is shown

in Figure 3.11. The test specimen is supported by two wires that can be positioned in

correspondence of the antinode lines. The specimen is excited by striking it with a small mass

attached to the extremity of a flexible bar. The frequencies excited are sensed by a microphone

connected to a spectrum analyzer. The analysis of the spectrum is done by means of the PAK

software.

Figure 3.11 IET set-up.

ASTM C1259: Standard test method for dynamic Young’s modulus, shear

modulus, and Poisson’s ratio for advanced ceramics by impulse excitation

of vibration (21)

The test method describes the procedure to determine the dynamic Young’s modulus, using the

resonant frequency in the flexural mode of vibration, and the dynamic shear modulus, using the

torsional resonant mode of vibration. The Poisson’s ratio is computed starting from these two.

Although the relationship between resonant frequency and dynamic modulus stated in the

standard are only valid for homogeneous, elastic and isotropic materials, the good practices and


57

recommendations are adopted for the tests carried out on the materials object of this study to

determine the resonant frequency. If anisotropy and inhomogeneity are considered it is also

possible to determine the elastic properties for these materials. Some of the key points of the

procedure are:

• Apparatus

o It consists of an excitation tool, a transducer to convert the mechanical vibration

into electrical signal, an electronic system (signal amplifier/conditioner, signal

analyzer and frequency readout device) and a support system.

o The impulse should induce a measurable mechanical vibration without

displacing or damaging the specimen. The transducer frequency range would be

100 Hz ÷ 50 kHz.

o The support should isolate the test specimen from outer vibration without

restricting the mode of vibration of interest. Test specimens should be supported

along the nodal lines.

• Test specimen:

o Its shape ratio shall be chosen so that the resonant frequency fall within the range

of measurement of the transducer.

o Its surfaces should be flat. Opposite surfaces across the length and width should

be parallel within 0.01 mm or ± 0.1%, opposite surfaces across the thickness

within 0.002 mm or ± 0.1%.

• Procedure

o (out-of-plane flexure) Place the non-contact transducer over an antinode point

close enough to sense the vibration of interest. Strike the specimen lightly and

elastically either at the center or at the edges.

o (torsional resonant frequency) locate the transducer over a quadrant of the

specimen, possibly at 0.224L from the end and near the edge. Strike the

specimen at the opposite quadrant, to minimize the excitation of the flexural

mode.

RESULTS

58

4 Results

In this chapter are stated the results of the thermo-physical and mechanical characterization

performed over the two materials objects of the thesis. Most of the charts show the measurement

of one sample, considered representative of the batch. In any case, the scatter between

measurements of the same kind of sample is within the instruments uncertainties.

4.1 CFC FS140®

4.1.1 Thermo-physical characterization

Thermal expansion and CTE

The thermal expansion is measured with the pushrod dilatometer described in 3.2.1 and the

CTE evaluated with the method explained in 2.1.3. A measurement of each sample has been

carried out with the parameters described in Table 3.8. Not all the samples received have been

tested as shown in Table 4.1, containing also the specimen’s length before and after the test.

RESULTS

59

Tested/received Initial length [mm] Final length [mm]

yz 3/6 Sample 1 25.023 25.023

Sample 2 25.040 25.038

Sample 3 25.043 25.048

x 3/6 Sample 1 25.058 25.060

Sample 2 25.074 25.089

Sample 3 25.038 25.044

Reference

temperature

Heating phase: 30℃

Cooling phase: 40℃ Table 4.1 CFC FS140® dilatometry samples details.

The graphs below depict the thermal expansion and CTE against the temperature, for 𝑦𝑧 and 𝑥

samples, measured during the heating and cooling phases. For easy of exhibition only one curve

per set of samples is shown: the maximum deviation of the other two samples is stated for each

case in the corresponding caption.

Figure 4.1 Thermal expansion against temperature for a yz sample of CFC FS140®, in the heating and cooling

phases. Max deviation from these values is 5.3 10-3 %.

RESULTS

60

Figure 4.2 Coefficient of thermal expansion versus temperature for a yz sample of CFC FS140®, evaluated

during the heating and cooling phases. Max deviation from these values is 0.33 10-6 K-1 during heating and 0.11

10-6 K-1 during cooling.

Figure 4.3 Thermal expansion against temperature for a x sample of CFC FS140®, in the heating and cooling

phases. Max deviation from these values 2%.

RESULTS

61

Figure 4.4 Coefficient of thermal expansion versus temperature for a x sample of CFC FS140®, evaluated during

the heating phase. Max deviation from these values is 0.44 10-6 K-1 during the heating phase and 0.28 10-6 K-1

during the cooling phase.

Specific heat

The calorimetry analysis has been performed with the differential scanning calorimeter

described in 3.2.3, and the specific heat evaluated with the method described in 2.1.2. The

overview of the tested samples is listed in Table 4.2, while the test parameters are stated in

Table 3.12.

Tested/received Mass [mg]

3/6

Sample 1 24.6

Sample 2 24.7

Sample 3 25.4

Reference material POCO graphite 40.6 mg Table 4.2 CFC FS140® calorimetry samples details.

Every specimen has been tested three times but in the graphs below only the average of these

three tests is reported for each sample. The maximum standard deviation between

measurements over the same sample is 0.04 J/gK.

RESULTS

62

Figure 4.5 Average curves of specific heat vs temperature for three different CFC FS140®.

Thermal diffusivity and thermal conductivity

The thermal diffusivity is measured by means of the laser flash apparatus described in 3.2.2

applying the Cape-Lehman model explained in 2.1.6. The test parameters are stated in Table

3.10. The thermal diffusivity is inversely proportional to the specimen’s thickness to the square

power: as the temperature increase the thickness changes accordingly to the coefficient of

thermal expansion. This is taken into account using the CTE values measured through

dilatometry: for the 𝑦𝑧 LFA samples, the thickness variation is calculated with the CTE

measured in the 𝑥 direction and vice versa. In Figure 4.6 and Figure 4.7, is shown the thermal

diffusivity variation with temperature for three different samples in the two directions. Every

sample has been tested once.

RESULTS

63

Figure 4.6 Thermal diffusivity vs temperature of three CFC FS140® yz samples.

Figure 4.7 Thermal diffusivity vs temperature of three CFC FS140® x samples.

RESULTS

64

The thermal conductivity is calculated starting from the measured thermal diffusivity, with

equation 2.20, here stated again for clarity: 𝜆(𝑇) = 𝛼(𝑇)𝜌(𝑇)𝑐𝑝(𝑇), where 𝛼(𝑇) is the thermal

diffusivity, 𝜌(𝑇) is the density and 𝑐𝑝(𝑇) the specific heat. The specific heat values have been

measured by calorimetry up to ~700 ℃, while the range of measurement of the thermal

diffusivity ranges from room temperature to 1950 ℃: in the calculation of the thermal

conductivity the values of specific heat at temperature above 700 ℃ have been kept constant

and equivalent to the measured value at 700 ℃ (conservative hypothesis). Also, the density of

the material is a function of the temperature: the change in volume is taken into account by

correcting the diameter and the thickness of the sample with the measured values of CTE in the

corresponding directions. In Figure 4.8 and Figure 4.9, it is shown the thermal conductivity

calculated from room temperature to 1950 ℃.

Figure 4.8 Thermal conductivity vs temperature of three CFC FS140® yz samples.

RESULTS

65

Figure 4.9 Thermal conductivity vs temperature of three CFC FS140® x samples.

4.1.2 Mechanical characterization

Compression test

The compression tests were carried out using the universal testing machine and the

configuration described in 3.3.1, over three sample per direction machined with the geometry

stated in Table 3.1. The results of the tests are shown in the following Figure 4.10 and Figure

4.11. In the case of the 𝑥 samples (see Figure 4.11) the choice of the strain gauges was not

adequate because unable to bear such big deformation. Hence, the values of the compression

stresses to rupture are stated in the legend and in Table 4.3, which contains also the other

meaningful results of the compression tests.

Compressive properties Stress to rupture [MPa] Strain to rupture [µm/m]

yz Sample 1 94.4 1123

Sample 2 101.7 761

Sample 3 99.3 656

x Sample 1 92.6 -

Sample 2 86.6 -

Sample 3 90.1 - Table 4.3 Compressive properties of CFC FS140®. No data available for strain to rupture.

RESULTS

66

Figure 4.10 Compression stress vs strain of three CFC FS140® yz samples.

Figure 4.11 Compression stress vs strain of three CFC FS140® x samples.

In Figure 4.12 it is possible to appreciate the diverse kinds of fracture occurred in the 𝑦𝑧 and 𝑥

samples.

RESULTS

67

Figure 4.12 Diverse ways of fracture due to compression stresses in the CFC FS140® yz sample (left) and in the

x one (right).

Flexural test

The 4-point bending test was performed with the configuration described in 3.3.1, over three

samples per direction, cut in the shape stated in Table 3.1. In the pictures below, the results of

the tests.

Figure 4.13 Flexural stress vs strain of three CFC FS140® yz samples.

RESULTS

68

Figure 4.14 Flexural stress vs strain of three CFC FS140® x samples.

During the test over the “Sample 2 yz” and “Sample 3 yz” five loading/unloading cycles have

been performed to determine the Young’s modulus.

Flexural properties Stress to rupture [MPa] Strain to rupture [µm/m] E [GPa]

yz Sample 1 152.5 1980 -

Sample 2 182.0 3414 80

Sample 3 159.0 3150 66

x Sample 1 9.0 7152

- Sample 2 8.6 6084

Sample 3 8.2 1689 Table 4.4 Flexural properties of CFC FS140®.

The curves shown in Figure 4.14 corresponds to different tests conditions: for “Sample 1 𝑥”

and “Sample 2 𝑥” a pre-load of 20 N was set and the strain gauge output signal set to zero when

this preload was reached. Only at the end of the test, in the light of the total strain imposed,

resulted that the initial strain achieved during the preload was not negligible. Consequently for

“Sample 3” the pre-load was not applied. “Sample 2” initial point does not correspond to 0

µm/m because the strain gauge was not zeroed after the application of the pre-load.

In Figure 4.15 it is possible to appreciate the two different kinds of fracture for specimen when

the load is applied perpendicularly or in parallel to the planes of the CFs.

RESULTS

69

Figure 4.15 Diverse ways of fracture due to flexural stresses in the CFC FS140® yz sample (left) and in the x

one (right).

Impact excitation technique

The measurement of the resonant frequencies of the material was carried out using the

configuration described in 3.3.2. The tests are normally carried out over the same samples that

will then be used in the destructive bending test. A first attempt of determining the first flexural

mode of the material in the 𝑦𝑧 direction was done but it had been discarded in the light of the

E modulus values determined with the flexural test. Additional tests were carried out over spare

samples, to look for the modes of interest in a more suitable range of frequencies. Performing

the test was challenging due to the damping of the material and the limit of the electronics,

hence reliable results cannot be stated for this material.

70

4.2 MG-6403-Fc

4.2.1 Thermo-physical characterization

Thermal expansion and CTE

The thermal expansion is measured with the pushrod dilatometer described in 3.2.1 and the

CTE evaluated with the method explained in 2.1.3. A measurement of each sample has been

carried out with the parameters described in Table 3.8. The number of sample tested and their

initial and final length are stated in Table 4.5.

The graphs below depict the thermal expansion and CTE against the temperature, for 𝑦𝑧 and 𝑥

samples, measured during the heating and cooling phases. For the sake of clarity only one curve

per set of samples is shown: the maximum deviation of the other two samples is stated for each

case in the corresponding caption.

Tested/received Initial length [mm] Final length [mm]

yz 3/3 Sample 1 14.969 -

Sample 2 15.022 15.024

Sample 3 15.021 15.022

x 3/3 Sample 1 14.965 14.993

Sample 2 14.991 15.020

Sample 3 14.976 15.016

Reference

temperature

Heating phase: 30℃

Cooling phase: 40℃ Table 4.5 MG-6403-Fc dilatometry samples details.

RESULTS

71

Figure 4.16 Thermal expansion against temperature for a yz sample of MG-6403-Fc, in the heating and cooling

phases. Max deviation from these values is 22 10-3 %.

Figure 4.17 Coefficient of thermal expansion versus temperature for a yz sample of MG-6403-Fc, evaluated

during the heating and cooling phases. Max deviation from these values is 0.15 10-6 K-1.

RESULTS

72

Figure 4.18 Thermal expansion against temperature for a x sample of MG-6403-Fc, in the heating and cooling

phases. Max deviation from these values is 0.17 %.

Figure 4.19 Coefficient of thermal expansion versus temperature for a x sample of MG-6403-Fc, evaluated

during the heating and cooling phases. Max deviation from these values is 2 10-6 K-1.

RESULTS

73

Specific heat

The specific heat of the material has been determined following the method explained in 2.1.2,

with the differential scanning calorimeter described in 3.2.3. The temperature program is

described in Table 3.12, and the details of the test samples are in the following Table 4.6.

Tested/received Mass [mg]

3/3

Sample 1 39.4

Sample 2 39

Sample 3 40.6

Reference material Sapphire Table 4.6 MG-6403-Fc calorimetry samples details.

Every specimen has been tested three times but in the graphs below only the average of these

three tests is reported for each sample. The maximum standard deviation between

measurements over the same sample is 0.02 J/gK.

Figure 4.20 Average curves of specific heat vs temperature for three MG-6403-Fc samples.

Thermal diffusivity and thermal conductivity

The same method, instrument and test parameters used to measure the thermal diffusivity of the

CFC FS140® have been used to test this MoGR grade. Also in this case, the variation of the

specimen thickness is taken into account according to the CTE in the suitable direction. In

RESULTS

74

Figure 4.21 and Figure 4.22 is depicted the thermal diffusivity variation with the temperature

for multiple MG-6403-Fc samples along the two directions. One test has been carried out on

each sample.

Figure 4.21 Thermal diffusivity vs temperature of two MG-6403-Fc yz samples.

Figure 4.22 Thermal diffusivity vs temperature of four MG-6403-Fc x samples.

RESULTS

75

As for the CFC FS140®, the thermal conductivity has been evaluated with the formula 2.30.

The variation of density is corrected thanks to the CTE values measured through dilatometry in

the two directions. The specific heat has been measured from room temperature up to ~1000

℃: still being conservative, the value of specific heat used to evaluate the thermal conductivities

in the range between 1000 and 1950 ℃, has been kept constant and equal to its value at ~1000

℃. The resulting thermal conductivities variation with the temperature for samples in the two

directions are depicted in Figure 4.23 and Figure 4.24.

Figure 4.23 Thermal conductivity vs temperature of two MG-6403-Fc yz samples.

RESULTS

76

Figure 4.24 Thermal conductivity vs temperature of four MG-6403-Fc x samples.

4.2.2 Mechanical characterization

The mechanical characterization for this material consist in 4-point flexural tests and IET while

the compressive behavior has not been investigated.

Flexural test

The test method is described in 3.3.1 with the fixture shown in Figure 3.10, over four 𝑥 samples

and five 𝑦𝑧 samples. The flexural stress versus strain curves, whose relationship is modeled by

equation 2.41, are shown in the following Figure 4.25 and Figure 4.26. The values of maximum

flexural stress and strain for each sample are collected in Table 4.7

Flexural properties Stress to rupture [MPa] Strain to rupture [µm/m]

yz Sample 1 60.7 2763

Sample 2 65.9 2155

Sample 3 65.6 3027

Sample 4 48.5 1620

Sample 5 49.7 2610

x Sample 1 10.4 4685

Sample 2 11 4486

Sample 3 10 5544

Sample 4 11.8 2720 Table 4.7 Flexural properties of MG-6403-Fc.

RESULTS

77

Figure 4.25 Flexural stress versus strain for five MG-6403-Fc yz samples.

Figure 4.26 Flexural stress versus strain for four MG-6403-Fc x samples.

RESULTS

78

Impact excitation technique

The IET measurements have been done over the same samples available for the flexural tests.

The method adopted is described in 2.2.2 while the set-up is shown in Figure 3.11. The first

flexural modes were excited during the tests and their frequencies are stated in Table 4.8 and

Table 4.9, together with the dimensions of the test specimens and the estimation of the Young’s

modulus in the hypothesis of elastic, homogeneous and isotropic material.

Sample yz m [g] L [mm] b [mm] t [mm] ff [kHz] E [GPa]

1 1.51 24.81 5.05 4.85 36.9 60.7

2 1.44 24.79 5.03 4.54 39.23 70.1

3 1.45 24.82 5.07 4.59 37.64 63.2

4 1.52 24.80 5.07 4.84 37.01 60.9

5 1.47 24.82 5.05 4.67 36.04 58.1 Table 4.8 Test specimens’ mass and sizes, first flexural frequency and estimation of the Young’s modulus

(isotropic, homogeneous and elastic material) measured for MG-6403-Fc yz samples.

Sample x m [g] L [mm] b [mm] t [mm] ff [kHz] E [GPa]

1 3.33 24.95 9.93 5.03 8.28 3.37

2 1.88 24.95 5.68 5.08 8.54 3.45

3 1.56 25.05 5.09 4.79 8.12 3.40

4 1.65 25.00 5.09 5.04 8.81 3.69 Table 4.9 Test specimens’ mass and sizes, first flexural frequency and estimation of the Young’s modulus

(isotropic, homogeneous and elastic material) measured for MG-6403-Fc x samples.

DISCUSSION

79

5 Discussion

In this part, the results shown in the previous chapter are discussed and analyzed from the point

of view of the collimators’ jaws required performances. The FoMs are evaluated and the critical

properties compared with those of the previously developed materials.

5.1 CFC: general aspects

The CFC FS140® provided by the Japanese Tatsuno has been fully characterized both from the

thermal and mechanical point of view, except for the IET analysis. The results obtained were

in line with the expectation and the literature values stated for this composite. From the thermal

point of view the material shows a very low CTE, typical of CFCs, which is negative in the

direction parallel to the fibers up to ~ 1000 ℃ and below 0.7 10−6𝐾−1 at higher temperatures.

In the direction 𝑥, perpendicular to the fibers it is below 11 10−6 𝐾−1. The calorimetry analysis

was limited to ~ 700 ℃, due to excessive noise in the DSC output signal: this results in non-

ideal repeatability of the measurements. The noise was due to both oxidation and aged sample

holder/furnace control issue. The values of specific heat at 25 ℃ were extrapolated from the cp

vs temperature curves and its average value is 717 𝐽/𝑘𝑔𝐾. Previous to the LFA analysis the

samples were used to measure the density by means of an Archimedes’ scale: during the

measurement of the weight of the sample submerged in the ethanol, some liquid infiltrated in

the voids of the materials, resulting in a slightly higher measured density. To avoid effects in

the thermal diffusivity measurements the specimens were dried in a kiln at ~ 100 ℃ for almost

DISCUSSION

80

2 hours. The following LFA tests resulted unaffected. The thermal diffusivity is highly affected

by the orientation: in the direction parallel to the fibers it is almost three times higher than

perpendicularly: this fact, which also occurs in the MoGR composites, is linked to the properties

of the graphene layers which are highly conductive in-plane and poorly conductive in the

direction perpendicular to the planes. The same principle is valid when referring to the electrical

conductivity: the measurements of electrical conductivity carried out in another laboratory

following the standard test method ASTM C611 are stated in Table 5.1. The measurements

were carried out perpendicularly and in two orthogonal direction in the plane: this was done

because the currently used CFC AC150® showed anisotropy in the planes. The tests show that

also CFC FS140® has different values of electrical conductivity in the plane.

As for the mechanical characterization, for the 𝑥 samples it was not possible to obtain the strain

to rupture in compression by means of the strain gauges which were not adequate to bear the

strain occured. Consequently, the stress vs strain curves are incomplete and only the stresses to

rupture could be measured. The Young’s modulus evaluated with the IET cannot be stated with

a known uncertainty due to the high damping of the material, which caused issues in the

identification of the resonant frequencies. The material shows also radically different

mechanical behaviors in the directions parallel and perpendicular to the fibers. The fibers act

as a reinforcement, as can be deducted from the results of the flexural tests: the flexural stress

to rupture measured for the parallel specimens ranges between 150 − 180 𝑀𝑃𝑎. These values

are more than 10 times higher than those measured in the perpendicular samples. The latter

presents higher elongation. In Figure 4.15 it is clear how the fractures occurred in the two

specimens. In the 𝑦𝑧 one the failure was due to the achievement of the admissible maximum

stress of the fibers, which broke in distinct locations and resulted in a jagged surface. In the 𝑥

samples the fracture consisted in the separation of layers, which are bonded with weak forces

and results in a flat and uniform surface parallel to the basal planes. The material shows also

higher stiffness in the direction of the fibers and the strain to rupture in this direction is almost

half than that achievable in the perpendicular samples. The stress to rupture in compression has

similar values in the two directions, since the fibers act as a reinforcement under tensile stresses.

Therefore, in compression the behavior is mostly driven by the mechanical properties of the

graphitic matrix. In the 𝑦𝑧 direction, the material shows a higher stiffness and the strain to

rupture is limited: in Figure 4.12 it is possible to distinguish, as for the flexural tests, two diverse

types of fracture. In the 𝑦𝑧 specimens, the fracture propagated along the planes that in this case

were parallel to the loading direction. The 𝑥 specimens showed a different surface of fracture

typical of brittle materials. The higher strain achieved in the 𝑥 samples can be explained

DISCUSSION

81

considering that the compression load is applied perpendicularly to the planes and tends to

compact them, closing the voids, until the maximum admissible stress of the graphitic matrix

is reached.

5.2 CFC: comparison

It is of paramount interest to compare the results of the characterization of CFC FS140® with

those of the currently employed CFC AC150®, which was characterized in the Mechanical

measurement laboratory in 2015. Some generic differences were known even before the

characterization: the use of a different raw graphite, since Tatsuno changed the provider, which

was the reason that justified the new characterization, and the final baking temperature. CFC

AC150® was baked at 2800 ℃ while CFC FS140® at 2500 ℃. From this latter information, it

is possible to anticipate, prior to the tests, an expected lower thermal (and electrical)

conductivity, that depends on the level of carbonization which in turn increases with the

temperature. This expectation is confirmed by the measurements, as shown in Figure 5.1 and

Figure 5.2:

Figure 5.1 Comparison between CFC FS140® and CFC AC150® in terms of thermal diffusivity (red) and

thermal conductivity (blue) in the yz direction.

DISCUSSION

82

Figure 5.2 Comparison between CFC FS140® and CFC AC150® in terms of thermal diffusivity (red) and

thermal conductivity (blue) in the x direction.

In the samples cut in the direction parallel to the fibers plane the thermal conductivity of the

CFC FS140® is ~74% lower than the currently used CFC AC150®. The same decrease of

properties can be noticed also for the electrical conductivity, in the three directions, as shown

in Table 5.1.

Electrical

conductivity [MS/m]

CFC AC150® CFC FS140®

x 0.03 0.02

y 0.24 0.12

z 0.18 0.09 Table 5.1 Electrical conductivity of CFC FS140® and CFC AC150®. In the best direction, the electrical

conductivity results ~50% lower than the older CFC.

From the thermal behavior point of view, only the thermal diffusivity/conductivity shows a

substantial difference between the two materials while the other properties are comparable, as

summarized in Table 5.2.

DISCUSSION

83

Property Unit CFC AC150® CFC FS140®

Density at RT g/cm3 1.86-1.90 1.85-1.90

Specific heat 25 C J/gK

0.755 0.724

500 C 1.614 1.593

CTEyz RT-200 C

10-6 K-1

-0.8 -0.97

RT-500 C -0.39 -0.51

RT-1000

C 0.03 -0.07

RT-1900

C 0.68 0.62

CTEx RT-200 C

10-6 K-1

10.88 9.32

RT-500 C 11.17 9.54

RT-1000

C 11.64 9.93

RT-1900

C 12.75 11.1

Thermal

diffusivityyz

20 C mm2/s

174 94

500 C 42 30

Thermal

diffusivityx 20 C

mm2/s 40 31

500 C 10 9.6

Thermal

conductivityyz 20 C

W/mK 233 124

500 C 126 85.7

Thermal

conductivityx 20 C

W/mK 54 42.5

500 C 30 29

Table 5.2 Comparison of thermal properties between the CFC FS140® and CFC AC150®.

The mechanical characterization of CFC AC150® consisted in the flexural and compression

tests. The comparison done with the available parameters is summarized in Table 5.3:

Property Unit CFC AC150® CFC FS140®

Flexural

strength

yz MPa

104 165

x 10 8.6

Flexural strain

to rupture

yz µm/m

1995 2850

x 4287 4980

Compression

strength

yz MPa

70 98

x 55 90

Compression

strain to

rupture

yz

µm/m - 847

x - -

Elastic

modulus, E

yz

GPa 62 73

x - -

Table 5.3 Comparison of mechanical properties between the CFC FS140® and CFC AC150®.

DISCUSSION

84

The new material shows slightly higher flexural properties in the direction of the fibers and

higher strength in compression. In order to assess and compare the performance of the materials

once embarked in the collimator’s jaw the FoMs are evaluated.

FoM CFC AC150® CFC FS140®

TRI 1372 1943

TSI 47 28 Table 5.4 FoMs for CFC AC150® and CFC FS140®.

Despite the much lower thermal conductivity, the higher strength and strain to rupture lead to

a more robust material with respect to the older one. On the other hand, the other two indexes,

electrical conductivity and TSI, are lower for the new CFC FS140® and indicate a less stable

material with a two times higher RF impedance.

5.3 MoGR

During both the thermo-physical and mechanical characterization of MG-6403-Fc, no particular

issue or unexpected results were encountered, therefore the most interesting aspect is the

comparison with the previously developed materials. Among these, two promising grades are

chosen for the comparison: MG-6403-Ga and MG-6451-Aa, whose composition and

production parameters are described in 1.6.2. The main difference in the production process

between the two old grades and the one object of the characterization consists in the temperature

of post-sintering. For MG-6403-Fc the post-sintering temperature was 2600 ℃ against the 2100

℃ of its predecessors. This temperature is above the melting point of the molybdenum carbides,

which in this step would melt again but in a pressure less condition. This might release the

internal stresses raised during the hot-pressing cycle. To better understand this effect, it is useful

to compare the residual deformation of the materials. Specifically, the residual deformation is

here conventionally defined as the change of length measured on the dilatometry specimens

after the dilatometry tests. The results, reported in Table 5.5, suggest that higher temperatures

of post-sintering allow more release of internal stresses. The measurements show also that the

material is always geometrically more stable in the direction parallel to the basal planes (𝑦𝑧).

DISCUSSION

85

Material Residual deformation (%)

MG-6403-Ga yz 0.02

x 0.18

MG-6541-Aa yz 0.02

x 0.14

MG-6403-Fc yz < res.

x 0.12 Table 5.5 Residual deformation of the dilatometry specimens for the three MoGR grades considered.

The other thermo-physical properties (together with the electrical conductivity) are collected in

Table 5.6.

Property Unit MG-6403-Ga MG-6451-Aa MG-6403-Fc

Density at RT g/cm3 2.492 2.490 2.586

Specific heat 25 C

J/gK 0.604 0.643 0.624

500 C 1.369 1.505 1.325

CTEyz

RT-200

C

10-6 K-1

2.03 2.31 2.56

RT-500

C 2.32 2.44 2.91

RT-

1000 C 2.24 2.27 2.95

RT-

1900 C 2.08 2.06 2.73

CTEx

RT-200

C

10-6 K-1

9.26 10.04 8.57

RT-500

C 10.2 11.04 9.32

RT-

1000 C 12.49 13.55 11.09

RT-

1900 C 17.52 18.43 15.36

Thermal

diffusivityyz

20 C mm2/s

364 317 353

500 C 75.4 74.5 70.7

Thermal

diffusivityx

20 C mm2/s

37.0 28.1 30.6

500 C 7.0 5.4 5.9

Thermal

conductivityyz

20 C W/mK

547 507 547

500 C 257 279 241

Thermal

conductivityx

20 C W/mK

55.7 44.9 47.4

500 C 23.8 20.1 20.3

Electrical

conductivityyx 25 C MS/m 0.88 0.98 0.91

Electrical

conductivityx 25 C MS/m 0.08 0.06 0.07

Table 5.6 Comparison of thermo-physical properties and electrical conductivity between three MoGR grades.

DISCUSSION

86

Overall the new grade MG-6403-Fc shows thermo-physical properties in line with those of the

previous developed grades: the specific heat, thermal diffusivity, thermal conductivity and

electrical conductivity are in between those of the predecessors. The materials result slightly

denser and it has a higher CTE in the parallel direction, while it is lower in the perpendicular

direction. The latter fact suggests a more isotropic nature.

The mechanical properties are listed below:

Property Unit MG-6403-Ga MG-6451-Aa MG-6403-Fc

Flexural

strength

yz MPa

73.5 79.5 61.1

x 11.6 12.4 8.1

Flexural

strain to

rupture

yz

µm/m 2643 1910 2161

x 4431 7065 4881

Elastic

modulus, E

yz

GPa 64.9 85.8 61.4

x 4.1 4.5 3.7

Table 5.7 Comparison of mechanical properties between three MoGR grades.

The material shows a flexural strength about 20% lower than the stronger grade and a modulus

of elasticity about 30% smaller than the stiffer one. The analysis of these data shows that the

addition of CF to the grade MG-6541-Aa, results in a higher strength but also a greater stiffness.

To compare the grades in terms of performance when employed as collimators absorbing

materials it is necessary to evaluate their FoMs, see Table 5.8:

FoM MG-6403-Ga MG-6451-Aa MG-6403-Fc

TRI 274.1 226 237

TSI 43.3 37.4 42.6 Table 5.8 FoMs for MG-6403-Ga, MG-6541-Aa and MG-6403-Fc.

Among the previous grades of MoGR, the candidate MG-6403-Fc averages the two

predecessors. With respect to MG-6403-Ga it shows both lower TRI and TSI. TRI is lower due

to the higher expansion and slightly lower strength, while the TSI is smaller because of the

higher density and the lower thermal conductivity. Despite showing the best mechanical

properties, the grade MG-6451-Aa has the lower TRI index, explainable with the higher CTE

(in both directions). The overview of the performance parameters suggests that the modification

of some production variables adopted to realize the new MG-6403-Fc (that has the same

composition of MG-6403-Ga), doesn’t bring to a more performing material. Therefore,

improvement of this material should be sought in other aspects, such as ultra-high vacuum

performances and radiation hardness.

CONCLUSIONS

87

6 Conclusions

Two ceramic-matrix composites, candidate for their use in the primary and secondary

collimators jaws of the LHC, were characterized and assessed in terms of Figures of Merit, to

rank their performances once embarked in the collimators. CFC FS140®, produced by the

Japanese Tatsuno, is considered, since the CFC AC150®, also produced by the Asiatic

company, had already been successfully employed for beam cleaning purposes at CERN.

Carbon fibers – carbon materials show a good beam impact robustness and are often suitable

materials for thermal management and nuclear plants devices. The reason which lead to a new

characterization of the CFC was the different raw material and thermal treatment chosen by

Tatsuno in recent years. The other material object of the study, MG-6403-Fc, is a molybdenum

carbide reinforced graphite, realized within a collaboration with the Italian SME BrevettiBizz,

that gave birth during years to more than 15 materials. The aim of the collaboration is to develop

materials with some qualities typical of ceramic composites, such the already mentioned beam

impact resistance but also low coefficient of thermal expansion, and increased thermal and

electrical conductivities, the latter being of paramount importance to reduce the radio frequency

impedance of the devices. After describing the models and the principles behind the measuring

technique, the instruments and the test parameters are developed and finally the results of the

characterization of both materials are stated.

The results of the analysis of the CFC FS140® shows some worse properties with respect to the

older one. Both thermal and electrical conductivity are lower: at room temperature, the thermal

conductivity is ~74% lower and the electrical conductivity ~50% lower. This can be explained

CONCLUSIONS

88

with a lower level of graphitization of the newer material, as a consequence of the lower final

baking temperature: 2500 ℃ against 2800 ℃ of the CFC AC150®. On the other hand, the

material shows increased mechanical properties, both in terms of flexural and compressive

strength and elasticity modulus.

The development of the molybdenum carbide graphite leads actually to materials with the

desired properties: generally, these materials show low enough CTE and higher thermal and

electrical conductivity than CFCs (up to 5 times higher electrical conductivity). The liquid

phase sintering process, permits to obtain high densification, thanks to the infiltration of liquid

carbides in the voids, and catalytic graphitization, responsible of the highly oriented graphitic

matrix. The results of MG-6403-Fc characterization are compared to those of two previously

developed promising grades, with similar composition but slightly different production process

(in the newer the post-sintering temperature is above the melting temperature of the

molybdenum carbides and the atmosphere is air). Overall the material shows similar behavior

and mean values of TRI and TSI, suggesting to look for improvement in other parameters of

the synthesis.

The following Table 6.1 collect the FoMs of the tested material CFC FS140® and MG-6403-

Fc, of the currently used CFC AC150® and of two others promising MoGR grades.

FoM CFC AC150® CFC FS140® MG-6403-Ga MG-6451-Aa MG-6403-Fc

TRI 1372 1943 274.1 226 237

TSI 47 28 43.3 37.4 42.6

RFI 0.24 0.12 0.88 0.98 0.91 Table 6.1 Overview of the FoMs for the tested materials (CFC FS140® and MG-6403-Fc), the currently

employed CFC AC150® and two other promising MoGR grades.

It is important to notice that both the CFC and MoGR are valid material for their use in the

primary and secondary collimator and the choice of one of them does not discard the use of the

other one. Nowadays, more than 100 collimators are installed and among these, for example,

there are more than seven different versions of primary and secondary collimators. In fact, being

impossible to find a jaw material with all the desired properties, it is often necessary to use

different material in combination. Therefore, while a baseline is fixed a small number of special

collimators would be installed in key point of the LHC to perform specific tasks, without

affecting the overall collimation system performance. Moreover, the FoMs are not the criteria

of choice among the materials but they represent a first criteria to select that materials worth to

be simulated and submitted to further tests, like the outgassing test. So far, the baseline of the

production of the new primary and secondary collimators has been identified with a grade of

CONCLUSIONS

89

MoGR, while the CFC ones would be produced as backup or where a lower dense collimator

jaws is needed.

Future works

In the light of the results obtained, further steps must be done:

• Order another grade of CFC baked at higher temperature, to check if the thermal and

electrical conductivity increase to acceptable values.

• Perform the tests over CFC along two directions in the plane of the fibers, due to the

anisotropy found during the characterization of the old CFC AC150® and also during

the current electrical conductivity measurements.

• Focus the parametric studies of the production of MoGR according to the latest results.

At CERN, in the framework of this R&D project, further investigations of the beam intercepting

devices’ materials are carried out, for example the observation of their behaviors when

subjected to the proton beam. Experiments run in the High Radiation to Materials (HiRadMat)

facility, are periodically conducted on the most promising batches of materials, and the next

one is scheduled for fall 2017. In this facility, high-intensity pulsed beams (440 GeV) are

provided to an irradiation area were materials samples are arranged inside a structure similar to

the one in Figure 6.1.

Figure 6.1 Overview of the HRMT-14 experiment test bench.

CONCLUSIONS

90

The samples are instrumented by the Mechanical measurement laboratory, which by means of

thermocouples, strain gauges, high speed camera and laser doppler vibrometer, is able to

provide data about shock waves, deformation, vibration, temperature increase and heat

dissipation. The two materials object of this study, will be tested in the facility and the results

of the observation will be of paramount importance to validate and develop the models, and to

experience the actual behavior under operation and catastrophic scenario.

Currently it is also possible to perform mechanical tests (tensile, compression and bending tests)

from room temperature to 1200 ℃, thanks to the recent implementation of an electric furnace

and laser extensometer system on the universal testing machine Zwick Z400 already installed

in the mechanical measurement laboratory. This will allow to track the mechanical properties

modification of the materials with the temperature in the range of temperatures actually reached

during operation in the collimators.

APPENDIX

91

Appendix

APPENDIX

92

Working principle of a thermocouple

A thermocouple is a transducer that senses temperature gradient and converts it in an electric

signal. The thermocouple is an electrical circuit realized with two conductors, made of different

materials, which are joined at one of their extremities. The physical principle at the basis of its

functioning is the Seebeck effect: when there is a temperature difference between the ends of

the described circuit, a potential difference arises. This effect is also known as thermoelectric

effect.

Figure A. 1 Scheme of a thermocouple: hot weld on the left side and cold junction of the right side.

The point where the conductors are joint is called measurement junction or hot weld, and it is

the sensitive part of the sensor. The other two extremities represent the cold junction, and it is

where the potential difference is measured. The hot weld is at the unknown temperature 𝑇𝑠𝑒𝑛𝑠𝑒,

while the cold junction is at a reference (known) temperature 𝑇𝑟𝑒𝑓. The potential difference is

proportional to the temperature gradient between the two junctions in a non-linear fashion:

∆𝑇 = ∑ 𝑎𝑛𝑉𝑛

𝑁

𝑖=1

Where the coefficients 𝑎𝑛 depend on the materials used and 𝑁 is chosen according to the level

of precision desired. There are several different types of thermocouples, made out of different

combinations of alloys, whose use depends upon melting point, chemical properties, stability,

cost, output etc. The types installed in the instrument employed for the characterization are

described in the table below.

Type Instrument Materials Output [mV/℃] Range of temperature

W3%Re-

W25%Re LFA, DIL

Tungsten -

Rhenium 4 0 - 2325 ℃

S DSC Platinum -

Rhodium 7 0 - 1650 ℃

APPENDIX

93

Working principle of a LVDT

The linear variable differential transformer is an electromechanical transducer which converts

a linear displacement into an electrical signal. It is an absolute output device: in case of power

cut the output signal after the restarting remains the same than before. Consequently, the null

point repeatability is extremely high. This sensor is composed by three solenoidal coils placed

around a tube in which a ferromagnetic core can move, see Figure A. 2. The central coil is the

primary, the two lateral are the top and bottom secondary coils, and they are simetrically

positioned with respect to the primary. The core is mechanically linked to the object whose

displacement is of interest.

Figure A. 2 LVDT’s components and electrical circuits scheme. Credits (22).

The primary coil is driven by an AC current of constant amplitude and frequency ranging

between 1 to 10 kHz: this generates an alternating magnetic field which induces an electric

signal on the two secondary coils, depending on the position of the core. When the core is at

the center, the same voltage is induced on the secondary coils, and the output signal is zero. As

the core moves, the mutual inductions between the primary and the secondary coils differ and

the output signal is positive or negative according to the displacement direction. The output of

the LVDT is very linear within a specified range of core motion.

APPENDIX

94

Working principles of a strain gauge

The strain gauge is a sensor widely used to measure the strain of an object, converting the strain

in an electrical output signal. The most common type of strain gauge is composed by a metallic

foil pattern (3÷6 µm thick) embedded in an insulating support film. The working principle is

based on the definition of electrical resistance 𝑅 of a conductor:

𝑅 = 𝜌𝑒𝑙

𝐿

𝐴

Where 𝜌𝑒𝑙 is the electrical resistivity of the material, 𝐿 the length of the active coil and 𝐴 its

section area. When the strain gauge is glued on the test specimen it is subjected to the same

strain than the surface, therefore it changes its length and its cross section: if stretched it will

become longer and narrower.

Figure A. 3 Strain gauge. Credits HBM.

Measuring 𝑅 allows to evaluate the strain of the test piece. The sensitivity to the measured strain

is given by the gauge factor 𝐺𝐹:

𝐺𝐹 =∆𝑅/𝑅0

∆𝐿/𝐿0=

∆𝑅/𝑅0

∈

The gauge factor can be expressed as a function of the Poisson’s ratio of the conductor material:

𝐺𝐹 =∆𝜌/𝜌

∈+ 1 + 2𝜈

Measured strain are rarely larger than millistrain, which results in very small changes in 𝑅. To

measure tenths of Ohms, the strain gauge is configured in a Wheatstone bridge.

APPENDIX

95

Wheatstone bridge

The Wheatstone bridge is a two legs electrical circuit: one leg contains one known resistance

and the unknown resistance (for example the strain gauge), the other leg contains two known

resistances, one of them variable.

Figure A. 4 Wheatstone bridge circuit.

In Figure A. 4, 𝑉𝐺 is the voltage across the bridge (measured input quantity), 𝑅1 and 𝑅2 are the

known constant resistances, 𝑅𝑥 the unknown resistance of the component and 𝑅2 is the variable

resistance. The exciting voltage is 𝑉𝑠.

Kirchhoff’s first rule to junction B and D leads to:

𝐼3 + 𝐼𝐺 − 𝐼𝑋 = 0

𝐼1 − 𝐼𝐺 + 𝐼2 = 0

And Kirchhoff’s second rule to the loops ABD and BCD:

𝐼1𝑅1 + 𝐼𝐺𝑅𝐺 − 𝐼3𝑅3 = 0

𝐼2𝑅2 − 𝐼𝑋𝑅𝑋 − 𝐼𝐺𝑅𝐺 = 0

When the bridge is balanced, 𝐼𝐺 = 0 and the above equations lead to:

𝐼3𝑅3 = 𝐼1𝑅1

𝐼𝑥𝑅𝑥 = 𝐼2𝑅2

From which:

𝑅𝑋 =𝑅3𝑅2

𝑅1

APPENDIX

96

The measured tension in the bridge is:

𝑉𝐺 = (𝑅2

𝑅1 + 𝑅2−

𝑅𝑥

𝑅3 + 𝑅𝑥) 𝑉𝑠

The 𝑅2, can either be adjustable or not: when using strain gauges and resistance thermometer,

𝑅2 is normally not adjustable because it is faster to read the voltage across the bridge than to

adjust the resistance to balance the bridge.

APPENDIX

97

Working principle of a load cell

A load cell is an electro-mechanical transducer able to convert a force acting on it in an electrical

output signal. There are several types of load cell, based on different principle of sensing the

force. For example, resistive load cells correlate the entity of the force by measuring the induced

strain on the device, while capacitive load cells are based on the principle of change of

capacitance when a voltage is applied to the sensor. All the load cells used in the mechanical

characterization of MG-6403-Fc and CFC FS140® are resistive load cells relying on the

deformation measured through strain gauges. For example, in the load cell shown in Figure A.

5 four strain gauges have been installed and when the load F is applied, two of them will be in

compression and two in traction.

Figure A. 5 Load cell scheme and position of the strain gauges. (23)

The four strain gauges are installed in a Wheatstone bridge. Knowing the relationship between

the state of tension and strain in the points of installation of the gauges allows to correlate the

electrical reading of the bridge to the force applied.

APPENDIX

98

Uncertainty of a measurement

Measuring is not an exact science, and repeated measurement of the same dimension lead to

different values. All the results of a measurement are affected by errors, of unknown amplitude,

therefore the result of the measurement itself is dispersed around the “true" value of the

measurand. The uncertainty of a measurement expresses the lack of knowledge of the value of

the measurand. When reporting the result of a measurement it is always good practice to express

it as its best estimate plus/minus its uncertainty. Before describing the two types of

uncertainties, it is useful to recall some statistics definition:

Probability, p: a real number in the range 0-1, associated to a random event.

Random variable, X: a variable which can assume any of the values of a set, associated to a

probability distribution.

Probability distribution: a function that expresses the probability that a random variable takes

any given value or belong to a range of values

Distribution function, F: a function giving for every value x of the set the probability that the

random variable X is equal to or less than x.

𝐹(𝑥) = 𝑃𝑟(𝑥 ≤ 𝑋)

Probability density function, p(x): is the derivative of the distribution function. Example:

𝑃(𝑎 < 𝑥 < 𝑏) = ∫ 𝑝(𝑥)𝑑𝑥𝑏

𝑎

Expectation (expected value, mean), 𝝁:

for a discrete random variable 𝜇 = 𝐸(𝑥) = ∑ 𝑝𝑖𝑥𝑖𝑁𝑖=1

for a continuous random variable 𝜇 = 𝐸(𝑥) = ∫ 𝑥𝑝(𝑥)+∞

−∞

Variance, 𝝈𝟐: is the expectation of the square of the centered random variable.

𝜎2 = 𝐸[(𝑋 − 𝐸(𝑋))]

Standards deviation, 𝝈: √𝜎2

Gauss distribution (normal distribution):

APPENDIX

99

𝑝(𝑥) =1

√2𝜋𝜎exp (−

𝑥 − 𝜇

2𝜎2)

Confidence interval for Gauss distribution:

- 1σ: 𝑃[(𝜇 − 𝜎) < 𝑥 < (𝜇 + 𝜎)] = 68.3%

- 2σ: 𝑃[(𝜇 − 2𝜎) < 𝑥 < (𝜇 + 2𝜎)] = 95.5%

- 1σ: 𝑃[(𝜇 − 3𝜎) < 𝑥 < (𝜇 + 3𝜎)] = 99.7%

Estimation: operation of assigning, from the observation of in a sample, numerical values to

the parameters of a distribution chose as the statistical model of the population from which this

sample is taken.

Arithmetic mean, ��: it is an estimate for the expectation.

�� =1

𝑛∑ 𝑥𝑘

𝑛

𝑘=1

Estimation of the variance: 𝑠2(𝑥𝑖) =1

𝑛−1∑ (𝑥𝑖 − ��)𝑛

𝑘=12

Variance of the arithmetic mean: 𝑠2(��) =𝑠2(𝑥𝑖)

𝑛

Standard deviation: positive square root of the variance.

Covariance: represent the measure of the mutual dependence between two random variables 𝑦

and 𝑧.

𝑐𝑜𝑣(𝑦, 𝑧) = 𝐸[(𝑦 − 𝐸(𝑦))(𝑧 − 𝐸(𝑧))]

Degree of freedom, ν: 𝜈 = 𝑛 − 1

Type A uncertainty

Let’s consider the case in which 𝑛 independent observation of the measurand 𝑥𝑘 have been

done under the same conditions. The best estimate of the measurand is the arithmetic mean of

the observed values, ��. The experimental standard deviation of the mean, 𝑠(��) represent the

uncertainty associated to the best estimate of the measurand:

𝑠(��) =𝑠(𝑥)

√𝑛= √

1

𝑛(𝑛 − 1)∑(𝑥𝑘 − ��)2

𝑛

𝑘=1

APPENDIX

100

The result of the measurement can be reported as:

𝑥 = �� ± 𝑢𝐴 = �� ±𝑠(𝑥)

√𝑛

Relative uncertainty, 𝒖𝒓: 𝑢𝑟(𝑦) = 𝑢(𝑦)/��, it is dimensionless and allows to compare

uncertainties associated to measurand of different nature.

Expanded uncertainty, U: it refers to an interval of values around ��, where it is expected to

find the measurand with a certain probability.

𝑈 = 𝐾𝑢

Where 𝑘 is the coverage factor (for a Gauss distribution, 𝑘 = 2 produces an interval having a

level of confidence of 95%, 𝑘 = 3 of approximately 99%).

Type B uncertainty

If repeated measurements have not been taken, the estimate of the measurand and of its variance

must be done by scientific judgment based on available information, like:

- Previous measurement data

- Knowledge or experience of the behavior of the measurand

- Manufacturer’s specification

- Data provided in calibrations or other certifications

- Uncertainties assigned to reference data taken from handbook

It is needed to:

1. Define an interval around the expected value, with an associated probability to find the

values of the measurand.

2. Define a probability distribution function (example: Gauss, triangular or uniform)

3. Evaluate expectation, variance and standard deviation

Uniform probability distribution function: the interval around the expected value 𝑎0, has a

width of 2𝑎. The probability is:

𝑝(𝑥) = {

0, 𝑥 < 𝑎0 − 𝑎 1

2𝑎, 𝑎0 − 𝑎 < 𝑥 < 𝑎0 + 𝑎

0, 𝑥 > 𝑎0 + 𝑎

The other parameters are:

APPENDIX

101

𝜇(𝑥) = ∫ 𝑥1

2𝑎𝑑𝑥 = 𝑎0

+∞

−∞

𝜎2(𝑥) = 𝐸[(𝑥 − 𝜇(𝑥))] =∆𝑥2

12

𝜎 =∆𝑥

√12

Triangular probability distribution: the interval around the expected value 𝑎0 has a width of

2𝑎. The parameters of the distribution are:

𝜇(𝑥) = 𝑎0

𝜎2(𝑥) =∆𝑥2

24

𝜎 =∆𝑥

√24

The uncertainty of the triangular distribution is lower than the one of the uniform distribution.

Combined standard uncertainty

Direct measurement: 𝑢𝑐2(𝑥) = 𝑢𝐴

2(𝑥) + 𝑢𝐵2 (𝑥)

Indirect measurement

The quantity of interest 𝑦 rises from a combination of 𝑁 measured quantities 𝑥𝑖, which are the

input parameters:

𝑦 = 𝑓(𝑥1, 𝑥2, … , 𝑥𝑁)

The estimated value of 𝑦 is simply obtained substituting in 𝑓 the estimated 𝑥��. The uncertainty

of ��, is a combination of the uncertainty of the 𝑥𝑖.

𝑢𝐶 (𝑦) = √∑ (𝑑𝑓

𝑑𝑥𝑖)

2

𝑢2(𝑥𝑖) + 2 ∑ ∑ (𝑑𝑓

𝑑𝑥𝑖) (

𝑑𝑓

𝑑𝑥𝑗) 𝑢(𝑥𝑖 , 𝑥𝑗)

𝑁

𝑗=𝑖+1

𝑁−1

𝑖=1

𝑁

𝑖=1

Where we can define the sensitivity coefficient:

𝑐𝑖 = (𝑑𝑓

𝑑𝑥𝑖)

��

And the correlation coefficient:

APPENDIX

102

𝑟𝑖𝑗(𝑥𝑖,𝑥𝑗) =𝑢(𝑥𝑖, 𝑥𝑗)

𝑢(𝑥𝑖)𝑢(𝑥𝑗) ∈ [−1; 1]

𝑟𝑖𝑗 = 0 if the input parameter are statistically independent. With these coefficients it is possible

to write another expression for the combined uncertainty:

𝑢𝐶 (𝑦) = √∑ 𝑐𝑖2𝑢2(𝑥𝑖) + 2 ∑ ∑ 𝑐𝑖𝑐𝑗𝑟𝑖𝑗𝑢(𝑥𝑖)𝑢(𝑥𝑗)

𝑁

𝑗=𝑖+1

𝑁−1

𝑖=1

𝑁

𝑖=1

Specific cases:

• 𝒓𝒊𝒋 = 𝟎, independent variables: 𝑢𝑐(𝑦) = √∑ (𝑑𝑓

𝑑𝑥𝑖)

2

𝑢2(𝑥𝑖)𝑁𝑖=1

• �� = 𝒏𝟏��𝟏 ± 𝒏𝟐𝒙𝟐 ± ⋯ ± 𝒏𝑵��𝑵: 𝑢𝑐(𝑦) = √∑ 𝑛𝑖2𝑢2(𝑥𝑖) 𝑁

𝑖=1

• �� = 𝒙𝟏𝒏𝟏 ∗ ��𝟐

𝒏𝟐 ∗ … ∗ ��𝑵𝒏𝑵: 𝑢𝑟,𝐶(𝑦) = √∑ 𝑛𝑖

2𝑢𝑟2(𝑥𝑖)

𝑁𝑖=1 and if 𝑛𝑖 = ±1, 𝑢𝑟,𝐶(𝑦) =

∑ 𝑢𝑟2(𝑥𝑖)

𝑁𝑖=1 .

103

References

[1] https://cds.cern.ch/record/1092437/files/CERN-Brochure-2008-001-Eng.pdf, 14/01/2017

[2] https://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/beam.htm, 1401/2017

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magnets.htm, 14/01/2017

[4] S. Redaelli, https://lhc-collimation.web.cern.ch/lhc-

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upgrade-spec/Files/Misc/ABertarelli_HB2014_NovelMaterials_paper.pdf, 2014

[6] A. Oya, H. Marsh, “Review - Phenomena of catalytic graphitization”, Joural of materials

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[7] Harada, Y., “Graphite-Metal Carbide Composites”, 1966

[8] R. B. Matthews, G. M. Jenkins, “The high temperature interaction between molybdenum

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[9] O'Neill, M. J., “Measurement of specific heat functions by differential scanning

calorimetry”, Analytical Chemistry, vol. 38, no. 10, 1966

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[10] J. D. James, J. A. Spittle, S. G. R. Brown, R. W. Evans, “A review of measurement

techniques for the thermal expansion coefficient fo metals and alloys at elevated

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[11] W. J. Parker, R. J. Jenkins, C. P. Butler and G. L. Abbot, “Flash method of

determining thermal diffusivity, heat capacity and thermal conductivity”, Journal of

Applied Physics, vol. 32, no. 9, 1962

[12] Cowan, Robert D., “Pulse method of measuring thermal diffusivities at high

temperatures”, Journal of applied physics, vol. 36, no. 4, 1963

[13] Lehman, J. A. Cape and G. W., “Temperature and finite pulse time effects in the flash

method for measuring thermal diffusivity”, Journal of applied physics, vol. 34, no. 7,

1963

[14] Taylor, L. M. Clark and R. E., “Radiation loss in the flash method for thermal

diffusivity”, Journal of applied physics, vol. 46, no. 2, 1975

[15] J. D. Lord, R. Morrell, “Elastic modulus measurement”, Measurement Good Practice

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[16] ASTM International, “E228 -11 Standard test method for linear thermal expansion of

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[17] ASTM International, “E2585-09 Standard practice for thermal diffusivity by the flash

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[18] DEUTSCHE NORM, “DIN 51 007 General principles of differential thermal analysis”,

1994

[19] ASTM, “Standard test method for compressive strength of carbon and graphite”, 1991

[20] ASTM International, “ASTM C1161 Standard test method for flexural strength of

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[22] http://www.te.com/usa-en/industries/sensor-solutions/insights/lvdt-tutorial.html#chapter-

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http://www.te.com/usa-en/industries/sensor-solutions/insights/lvdt-tutorial.html#chapter-2-dl

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BIBLIOGRAPHY

106

Bibliography

N. Mariani, “Development of novel, advanced molybdenum-based composites for high

energy physics application”, Doctoral Dissertation, 2014

P. Di Marco, Handouts of Applied Thermofluidodynamics classes, 2006

Robert C. Juvinall, Kurt M. Marshek, “Machine Component Design”, Wiley, 5th Edition

International Student Version, 2012

Evaluation of measurement data — Guide to the expression of uncertainty in

measurement, JCGM 100:2008 GUM 1995 with minor corrections, First edition

September 2008

107

List of figures

Figure 0.1 Aerial view of the CERN site and accelerator complex.......................................... II

Figure 0.2 CERN’s accelerator complex. Credits CERN. ....................................................... III

Figure 0.3 Position of the collimators in the LHC................................................................... IV

Figure 0.4 Interaction between beam halo and collimator jaws. Credits S. Redarelli. (4) ....... V

Figure 0.5 Front view of the collimator jaws showing the aperture. ....................................... VI

Figure 0.6 Assembly of a collimator and collimator blocks. ................................................... VI

Figure 1.1 Graphite structure (6). .............................................................................................. 4

Figure 1.2 Reference system adopted for collimator, manufacturing process and sampling. ... 5

Figure 1.3 Image of a pitch-derived carbon fiber. ..................................................................... 7

Figure 1.4 SE image at high magnification of a graphite flake. ................................................ 9

Figure 1.5 Hot-pressing machine at BrevettiBizz...................................................................... 9

Figure 1.6 Molybdenum-Carbon phase diagram. The eutectic temperature MoC(1-x)-graphite

is at 2857 K (2584℃) (45 at% C) .................................................................................... 10

Figure 1.7 MoGR sintered plate. ............................................................................................. 11

Figure 2.1 Schematic of a DSC. Credits NETZSCH. .............................................................. 16

Figure 2.2 Temperature program and calculation of 𝒄𝒑. (9) ................................................... 17

Figure 2.3 Length of the sample as a function of temperature. ............................................... 18

Figure 2.4 Set-up for optical interferometers with the sample S in between two optical flats A

and B. (10) ........................................................................................................................ 20

Figure 2.5 Scheme of a horizontal push-rod dilatometer. ....................................................... 21

LIST OF FIGURES

108

Figure 2.6 Indicative thermal conductivity values at room temperature [W/mK]. Credits

NETZSCH. ....................................................................................................................... 24

Figure 2.7 Operative ranges of different measurements method for thermal conductivity.

Credits NETZSCH. ........................................................................................................... 25

Figure 2.8 Dimensionless plot of the rear surface. (11) .......................................................... 27

Figure 2.9 Normalized temperature rise of the rear face of the sample in function of time, for

different heat losses. ......................................................................................................... 29

Figure 2.10 Normalized temperature rise at the back surface. Curve 1 is for 𝝉 = 𝟎. 𝟎𝟏 𝒕𝒄,

curve 2 for 𝝉 = 𝟎. 𝟏 𝒕𝒄, curve 3 for 𝝉 = 𝟎. 𝟓𝟏𝒕𝒄 and curve 4 for 𝝉 = 𝟎. 𝟗𝟏𝒕𝒄. .............. 30

Figure 2.11 Scheme of a laser flash apparatus. ....................................................................... 31

Figure 2.12 Scheme of Voigt and Reuss assumption for a reinforced composite. .................. 32

Figure 2.13 Stress-strain curves representing brittle and ductile behaviors. ........................... 33

Figure 2.14 Out-of-plane vibration modes of a free-free beam: nodal lines. .......................... 35

Figure 2.15 Nodes and antinodes of the first out-of-plane flexural mode. .............................. 35

Figure 2.16 Torsional mode of a free-free prismatic beam: nodal lines. ................................. 36

Figure 2.17 Nodes and antinodes of the first torsional mode. ................................................. 36

Figure 2.18 Support and load application in the 3- and 4-point bending. ............................... 38

Figure 3.1 Picture of CFC FS140® test specimens for the thermo-physical (left) and

mechanical (right) characterization. ................................................................................. 41

Figure 3.2 SEM image of MG-6403-Fc sample cut along the x direction. ............................. 43

Figure 3.3 DIL 402 E by NETZSCH and its scheme. ............................................................. 44

Figure 3.4 Sample of POCO-Graphite housed in the sample holder with the Alumina set-up.

.......................................................................................................................................... 44

Figure 3.5 LFA 427 by NETZSCH with control cabinet, data acquisition system and laser

source and scheme of the measuring part. ........................................................................ 47

Figure 3.6 Sample holder and cap. .......................................................................................... 48

Figure 3.7 DSC Pegasus 404 C by NETZSCH and its schematic view. ................................. 50

Figure 3.8 Sample holder and OTS system. ............................................................................ 51

Figure 3.9 Universal testing machine Zwick Z400. ................................................................ 53

Figure 3.10 Fixture for the 4-point bending test. ..................................................................... 55

Figure 3.11 IET set-up. ............................................................................................................ 56

Figure 4.1 Thermal expansion against temperature for a yz sample of CFC FS140®, in the

heating and cooling phases. Max deviation from these values is 5.3 10-3 %. .................. 59

LIST OF FIGURES

109

Figure 4.2 Coefficient of thermal expansion versus temperature for a yz sample of CFC

FS140®, evaluated during the heating and cooling phases. Max deviation from these

values is 0.33 10-6 K-1 during heating and 0.11 10-6 K-1 during cooling. ......................... 60

Figure 4.3 Thermal expansion against temperature for a x sample of CFC FS140®, in the

heating and cooling phases. Max deviation from these values 2%. ................................. 60

Figure 4.4 Coefficient of thermal expansion versus temperature for a x sample of CFC

FS140®, evaluated during the heating phase. Max deviation from these values is 0.44 10-

6 K-1 during the heating phase and 0.28 10-6 K-1 during the cooling phase. ..................... 61

Figure 4.5 Average curves of specific heat vs temperature for three different CFC FS140®. 62

Figure 4.6 Thermal diffusivity vs temperature of three CFC FS140® yz samples. ................. 63

Figure 4.7 Thermal diffusivity vs temperature of three CFC FS140® x samples. ................... 63

Figure 4.8 Thermal conductivity vs temperature of three CFC FS140® yz samples. .............. 64

Figure 4.9 Thermal conductivity vs temperature of three CFC FS140® x samples. ............... 65

Figure 4.10 Compression stress vs strain of three CFC FS140® yz samples. ......................... 66

Figure 4.11 Compression stress vs strain of three CFC FS140® x samples. .......................... 66

Figure 4.12 Diverse ways of fracture due to compression stresses in the CFC FS140® yz

sample (left) and in the x one (right). ............................................................................... 67

Figure 4.13 Flexural stress vs strain of three CFC FS140® yz samples. ................................. 67

Figure 4.14 Flexural stress vs strain of three CFC FS140® x samples. ................................... 68

Figure 4.15 Diverse ways of fracture due to flexural stresses in the CFC FS140® yz sample

(left) and in the x one (right). ........................................................................................... 69

Figure 4.16 Thermal expansion against temperature for a yz sample of MG-6403-Fc, in the

heating and cooling phases. Max deviation from these values is 22 10-3 %. ................... 71

Figure 4.17 Coefficient of thermal expansion versus temperature for a yz sample of MG-

6403-Fc, evaluated during the heating and cooling phases. Max deviation from these

values is 0.15 10-6 K-1. ...................................................................................................... 71

Figure 4.18 Thermal expansion against temperature for a x sample of MG-6403-Fc, in the

heating and cooling phases. Max deviation from these values is 0.17 %......................... 72

Figure 4.19 Coefficient of thermal expansion versus temperature for a x sample of MG-6403-

Fc, evaluated during the heating and cooling phases. Max deviation from these values is

2 10-6 K-1. .......................................................................................................................... 72

Figure 4.20 Average curves of specific heat vs temperature for three MG-6403-Fc samples.73

Figure 4.21 Thermal diffusivity vs temperature of two MG-6403-Fc yz samples. ................. 74

Figure 4.22 Thermal diffusivity vs temperature of four MG-6403-Fc x samples. .................. 74

LIST OF FIGURES

110

Figure 4.23 Thermal conductivity vs temperature of two MG-6403-Fc yz samples. .............. 75

Figure 4.24 Thermal conductivity vs temperature of four MG-6403-Fc x samples. ............... 76

Figure 4.25 Flexural stress versus strain for five MG-6403-Fc yz samples. ........................... 77

Figure 4.26 Flexural stress versus strain for four MG-6403-Fc x samples. ............................ 77

Figure 5.1 Comparison between CFC FS140® and CFC AC150® in terms of thermal

diffusivity (red) and thermal conductivity (blue) in the yz direction. .............................. 81

Figure 5.2 Comparison between CFC FS140® and CFC AC150® in terms of thermal

diffusivity (red) and thermal conductivity (blue) in the x direction. ................................ 82

Figure 6.1 Overview of the HRMT-14 experiment test bench. ............................................... 89

111

List of tables

Table 1.1 CFC AC150® properties at room temperature along the three directions defined in

1.4. ...................................................................................................................................... 6

Table 1.2 Process and composition parameter for two different grades of MoGR. S =

sintering, PS = post sintering phases. ............................................................................... 11

Table 1.3 Tables of properties and FoMs at room temperature for the aforementioned

materials. Note that while for the MoGR grades the properties are given for the two

direction of anisotropy, the values for CFC results from the ROM (rule of mixtures)

average. For CFC properties along its main direction see Table 1.1................................ 13

Table 3.1 List of CFC FS140® samples’ dimensions and cutting directions. .......................... 41

Table 3.2 Density (average of three consecutive measurements) of four CFC FS140®

samples. The ambient temperature was 23 ℃ and the density of the medium (ethanol)

0.787 g/cm3. ...................................................................................................................... 42

Table 3.3 Composition of MG-6403-Fc. ................................................................................. 42

Table 3.4 Production process parameters. S=sintering, PS= post sintering. ........................... 42

Table 3.5 List of MG-6403-Fc samples’ dimensions and cutting directions. .......................... 42

Table 3.6 Density (average of three consecutive measurements) of two MG-6403-Fc samples.

The room temperature was 24 ℃ and the density of the medium (ethanol) 0.791 g/cm3.

.......................................................................................................................................... 43

Table 3.7 Key technical data of DIL 402 E. ............................................................................ 45

Table 3.8 Dilatometry test set-up. ............................................................................................ 45

LIST OF TABLES

112

Table 3.9 Key technical data of LFA 427 by NETZSCH. ....................................................... 48

Table 3.10 Laser flash test set-up. ........................................................................................... 49

Table 3.11 Technical data of the DSC Pegasus 404 C. ........................................................... 51

Table 3.12 Calorimetry test set-up. .......................................................................................... 51

Table 3.13 Features of the universal testing machine Zwick Z400. ........................................ 53

Table 3.14 Compression test parameters. ................................................................................ 54

Table 3.15 Bending test parameters. ........................................................................................ 55

Table 4.1 CFC FS140® dilatometry samples details. ............................................................... 59

Table 4.2 CFC FS140® calorimetry samples details. ............................................................... 61

Table 4.3 Compressive properties of CFC FS140®. No data available for strain to rupture. .. 65

Table 4.4 Flexural properties of CFC FS140®. ........................................................................ 68

Table 4.5 MG-6403-Fc dilatometry samples details................................................................ 70

Table 4.6 MG-6403-Fc calorimetry samples details. .............................................................. 73

Table 4.7 Flexural properties of MG-6403-Fc. ........................................................................ 76

Table 4.8 Test specimens’ mass and sizes, first flexural frequency and estimation of the

Young’s modulus (isotropic, homogeneous and elastic material) measured for MG-6403-

Fc yz samples. .................................................................................................................. 78

Table 4.9 Test specimens’ mass and sizes, first flexural frequency and estimation of the

Young’s modulus (isotropic, homogeneous and elastic material) measured for MG-6403-

Fc x samples. .................................................................................................................... 78

Table 5.1 Electrical conductivity of CFC FS140® and CFC AC150®. In the best direction, the

electrical conductivity results ~50% lower than the older CFC. ...................................... 82

Table 5.2 Comparison of thermal properties between the CFC FS140® and CFC AC150®. .. 83

Table 5.3 Comparison of mechanical properties between the CFC FS140® and CFC AC150®.

.......................................................................................................................................... 83

Table 5.4 FoMs for CFC AC150® and CFC FS140®. ............................................................. 84

Table 5.5 Residual deformation of the dilatometry specimens for the three MoGR grades

considered. ........................................................................................................................ 85

Table 5.6 Comparison of thermo-physical properties and electrical conductivity between

three MoGR grades. .......................................................................................................... 85

Table 5.7 Comparison of mechanical properties between three MoGR grades. ..................... 86

Table 5.8 FoMs for MG-6403-Ga, MG-6541-Aa and MG-6403-Fc. ...................................... 86

Table 6.1 Overview of the FoMs for the tested materials (CFC FS140® and MG-6403-Fc), the

currently employed CFC AC150® and two other promising MoGR grades. ................... 88

thermophysical and mechanical … · thermophysical and mechanical ... the goal of this project is...

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